# JEE Main & Advanced Mathematics Trigonometric Equations Question Bank

### done Solution of trigonometrical equations

• A) $2n\pi$

B) $n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{4}$

C) $2n\pi +\frac{\pi }{2}$

D) None of these

• A) $2n\pi \pm {{(-1)}^{n}}\frac{\pi }{6}$

B) $\frac{n\pi }{2}\pm {{(-1)}^{n}}\frac{\pi }{6}$

C) $n\pi \pm \frac{\pi }{6}$

D) $2n\pi \pm \frac{\pi }{6}$

• A) $2n\pi \pm \frac{\pi }{6}$

B) $n\pi \pm \frac{\pi }{6}$

C) $2n\pi \pm \frac{\pi }{3}$

D) $n\pi \pm \frac{\pi }{3}$

• A) $n\pi +\frac{\pi }{4}$

B) $\frac{n\pi }{2}+\frac{\pi }{8}$

C) $\frac{n\pi }{2}\pm \frac{\pi }{8}$

D) None of these

• A) $n\pi +{{(-1)}^{n}}\frac{\pi }{4}$

B) ${{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{3}$

C) $n\pi +\frac{\pi }{4}-\frac{\pi }{3}$

D) $n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{3}$

• A) $n\pi \pm \frac{\pi }{3}$

B) $2n\pi \pm \frac{\pi }{3}$

C) $2n\pi \pm \frac{\pi }{6}$

D) $n\pi \pm \frac{\pi }{6}$

• A) $n\pi +\frac{3\pi }{4}$

B) $2n\pi +\frac{\pi }{4}$

C) $2n\pi -\frac{\pi }{4}$

D) $2n\pi \pm \frac{\pi }{4}$

• A) $n\pi +\frac{\pi }{4}$

B) $n\pi -\frac{\pi }{4}$

C) $n\pi \pm \frac{\pi }{4}$

D) $2n\pi \pm \frac{\pi }{4}$

• A) $2n\pi \pm \frac{\pi }{3}$

B) $n\pi ,2n\pi \pm \frac{2\pi }{3}$

C) $n\pi ,2n\pi \pm \frac{\pi }{3}$

D) $n\pi ,\,\,n\pi +\frac{2\pi }{3}$

• A) $n\pi +\frac{\pi }{5}$

B) $\left( n+\frac{1}{6} \right)\frac{\pi }{5}$

C) $\left( 2n\pm \frac{1}{6} \right)\frac{\pi }{5}$

D) $\left( n+\frac{1}{3} \right)\frac{\pi }{5}$

• A) $\left( n+\frac{1}{2} \right)\frac{\pi }{3}$

B) $\left( n+\frac{1}{2} \right)\,\pi$

C) $\left( 2n\pm \frac{1}{2} \right)\frac{\pi }{3}$

D) None of these

• A) $n\pi +\frac{\pi }{2}$

B) $2n\pi -\frac{\pi }{2}$

C) $2n\pi +\frac{\pi }{2}$

D) None of these

• A) $2n\pi \pm \frac{\pi }{6}$

B) $n\pi \pm \frac{\pi }{6}$

C) $2n\pi \pm \frac{\pi }{3}$

D) $n\pi \pm \frac{\pi }{3}$

• A) $2n\pi +\frac{\pi }{6}$

B) $2n\pi \pm \frac{\pi }{6}$

C) $n\pi \pm \frac{\pi }{6}$

D) $n\pi \pm \frac{\pi }{3}$

• A) $\frac{n\pi }{4},\frac{n\pi }{3}+\frac{\pi }{18}$

B) $\frac{n\pi }{3},\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18}$

C) $\frac{n\pi }{4},\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18}$

D) $\frac{n\pi }{6},\frac{n\pi }{3}+{{(-1)}^{n}}\frac{\pi }{18}$

• A) $n\pi \pm \frac{\pi }{6}$

B) $n\pi +\frac{\pi }{6}$

C) $2n\pi \pm \frac{\pi }{6}$

D) None of these

• A) $n\pi \pm \frac{\pi }{3}$

B) $2n\pi \pm \frac{\pi }{6}$

C) $n\pi \pm \frac{\pi }{6}$

D) $2n\pi \pm \frac{\pi }{3}$

• A) $n\pi \pm \frac{\pi }{3}$

B) $n\pi \pm \frac{\pi }{6}$

C) $2n\pi \pm \frac{\pi }{3}$

D) $2n\pi \pm \frac{\pi }{6}$

• A) $n\pi +\frac{\pi }{4},n\pi +\frac{\pi }{3}$

B) $n\pi -\frac{\pi }{4},n\pi +\frac{\pi }{3}$

C) $n\pi +\frac{\pi }{4},n\pi -\frac{\pi }{3}$

D) $n\pi -\frac{\pi }{4},n\pi -\frac{\pi }{3}$

• A) $2n\pi +\alpha$

B) $2n\pi -\alpha$

C) $n\pi +\alpha$

D) $n\pi -\alpha$

• A) $2n\pi \pm \frac{\pi }{3}$

B) $2n\pi +\frac{\pi }{4}$

C) $n\pi \pm \frac{\pi }{3}$

D) $n\pi -\frac{\pi }{3}$

• A) $2n\pi \pm \frac{\pi }{6}$

B) $2n\pi \pm \frac{\pi }{3}$

C) $n\pi \pm \frac{\pi }{3}$

D) $n\pi \pm \frac{\pi }{6}$

• A) $2n\pi \pm {{\cos }^{-1}}\frac{-3+\sqrt{17}}{4}$

B) $2n\pi \pm {{\cos }^{-1}}\frac{-3-\sqrt{17}}{4}$

C) $n\pi \pm {{\cos }^{-1}}\frac{-3+\sqrt{17}}{4}$

D) $n\pi \pm {{\cos }^{-1}}\frac{-3-\sqrt{17}}{4}$

• A) A. P.

B) G. P.

C) H. P.

D) None of these

• A) $n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{3}$

B) $n\pi +{{(-1)}^{n}}\frac{\pi }{3}-\frac{\pi }{4}$

C) $n\pi +{{(-1)}^{n}}\frac{\pi }{3}+\frac{\pi }{4}$

D) $n\pi +{{(-1)}^{n}}\frac{\pi }{4}+\frac{\pi }{3}$

• A) $2n\pi -\frac{\pi }{4}\pm \,\,\alpha$

B) $2n\pi +\frac{\pi }{4}\pm \alpha$

C) $n\pi -\frac{\pi }{4}\pm \alpha$

D) $n\pi +\frac{\pi }{4}\pm \alpha$

• A) $n\pi$

B) $\frac{n\pi }{6}$

C) $n\pi -\frac{\pi }{4}\pm \alpha$

D) $\frac{n\pi }{2}$

• A) $n\pi +\frac{\pi }{4}$

B) $2n\pi +\frac{\pi }{4}$

C) $2n\pi -\frac{\pi }{4}$

D) $\frac{n\pi }{2}+{{(-1)}^{n}}\frac{\pi }{2}$

• A) $n\pi +\frac{\pi }{4}$

B) $n\pi +\frac{\pi }{4}$

C) $2n\pi \pm \frac{\pi }{4}$

D) $n\pi +{{(-1)}^{n}}\frac{\pi }{4}$

• A) $2n\pi +\frac{\pi }{4}$

B) $2n\pi \pm \frac{\pi }{4}$

C) $2n\pi -\frac{\pi }{4}$

D) None of these

• A) $\theta =n\pi +\frac{\pi }{2}-\alpha$

B) $\theta =n\pi -\frac{\pi }{2}+\alpha$

C) $\theta =n\pi +\frac{\pi }{2}+\alpha$

D) $\theta =n\pi -\frac{\pi }{2}-\alpha$

• A) $\frac{1}{2}[n\pi +{{(-1)}^{n}}{{\sin }^{-1}}(3/4)]$

B) $n\pi +{{(-1)}^{n}}{{\sin }^{-1}}(3/4)$

C) $\frac{n\pi }{2}+{{(-1)}^{n}}{{\sin }^{-1}}(3/4)$

D) None of these

• A) $\theta =2n\pi$

B) $\theta =\frac{2n\pi }{p\pm q}$

C) $\theta =\frac{n\pi }{p+q}$

D) None of these

• A) $x=n\pi \pm \frac{\pi }{2}$

B) $x=n\pi \pm \frac{\pi }{4}$

C) $x=n\pi \pm \frac{3\pi }{2}$

D) None of these

• A) $n\pi \pm \frac{\pi }{6}$

B) $n\pi \pm \frac{\pi }{3}$

C) $n\pi \pm \frac{\pi }{4}$

D) $n\pi \pm \frac{\pi }{2}$

• A) $n\pi +\frac{\pi }{4}$

B) $2n\pi \pm \frac{\pi }{4}$

C) $n\pi -\frac{\pi }{4}$

D) $2n\pi \pm \frac{\pi }{6}$

• A) $n\pi +{{(-1)}^{n}}\frac{\pi }{6}$

B) $n\pi +{{(-1)}^{n}}\frac{\pi }{2}$

C) $n\pi +{{(-1)}^{n}}\frac{5\pi }{6}$

D) $n\pi +{{(-1)}^{n}}\frac{7\pi }{6}$

• A) $2n\pi \pm \frac{\pi }{4}+\frac{\pi }{12}$

B) $n\pi +{{(-1)}^{n}}\frac{\pi }{4}+\frac{\pi }{12}$

C) $2n\pi \pm \frac{\pi }{4}-\frac{\pi }{12}$

D) $n\pi +{{(-1)}^{n}}\frac{\pi }{4}-\frac{\pi }{12}$

• A) $n\pi +\frac{\pi }{4}$

B) $\frac{n\pi }{3}+\frac{\pi }{12}$

C) $n\pi$

D) $n\pi \pm \frac{\pi }{4}$

• A) $\theta =n\pi +{{(-1)}^{n+1}}\frac{\pi }{3},\theta =n\pi ,n\in Z$

B) $\theta =n\pi ,n\in Z$

C) $\theta =n\pi +{{(-1)}^{n+1}}\frac{\pi }{3},n\in Z$

D) $\theta =\frac{n\pi }{2},n\in Z$

• A) $m\pi ,n\pi +\frac{\pi }{3}$

B) $m\pi ,n\pi \pm \frac{\pi }{3}$

C) $m\pi ,n\pi \pm \frac{\pi }{6}$

D) None of these (Where m and n are integers)

• A) $2\theta =\frac{\pi }{2}-\alpha$

B) $\theta =2n\pi \pm \left( \frac{\pi }{2}-\alpha \right)$

C) $\theta =\frac{n\pi +{{(-1)}^{n}}\alpha }{2}$

D) $\theta =n\pi \pm \left( \frac{\pi }{4}-\frac{\alpha }{2} \right)$

• A) $\frac{n\pi }{4}$or $n\pi \pm \frac{\pi }{3}$

B) $\frac{n\pi }{4}$or $n\pi \pm \frac{\pi }{6}$

C) $\frac{n\pi }{4}$or $2n\pi \pm \frac{\pi }{6}$

D) None of these

• A) $n\pi +{{(-1)}^{n}}\frac{\pi }{6}$

B) $2n\pi +\frac{\pi }{4}$

C) $n\pi +{{(-1)}^{n}}\frac{\pi }{2}$

D) $n\pi +{{(-1)}^{n}}\frac{\pi }{3}$

• A) $\theta =\frac{n\pi }{7}+\frac{\pi }{14}$

B) $\theta =\frac{n\pi }{7}+\frac{\pi }{5}$

C) $\theta =\frac{n\pi }{7}+\frac{\pi }{2}$

D) $\theta =\frac{n\pi }{7}+\frac{\pi }{3},n\in Z$

• A) $x=n\pi \pm {{\cos }^{-1}}(1/3)$

B) $x=2n\pi \pm {{\cos }^{-1}}(1/3)$

C) $x=n\pi \pm {{\cos }^{-1}}(1/6)$

D) $x=2n\pi \pm {{\cos }^{-1}}(1/6)$

• A) $\theta =2m\pi \pm \frac{2\pi }{3}$

B) $\theta =2m\pi \pm \frac{\pi }{4}$

C) $\theta =m\pi \pm {{(-1)}^{m}}\frac{2\pi }{3}$

D) $x=m\pi +{{(-1)}^{m}}\frac{\pi }{3}$

• A) $2n\pi \pm \frac{\pi }{6}$

B) $2n\pi \pm \frac{\pi }{4}$

C) $n\pi +{{(-1)}^{n}}\frac{\pi }{3}$

D) $n\pi +{{(-1)}^{n}}\frac{\pi }{4}$

• A) $(2n+1)\frac{\pi }{2}$

B) $n\pi$

C) $(2n+1)\frac{\pi }{2}$

D) $2n\pi$

• A) $\frac{\sqrt{5}-1}{4}$

B) $\frac{-\sqrt{5}-1}{4}$

C) 0

D) None of these

• A) $n\pi$

B) $n\pi \pm {{\sin }^{-1}}\frac{2}{5}$

C) $n\pi +\frac{\pi }{6}$

D) None of these

• A) $\frac{\pi }{3}(6k+1)$

B) $\frac{\pi }{3}(6k+1)$

C) $\frac{\pi }{3}(2k+1)$

D) None of these

• A) $\theta =n\pi$

B) $\theta =2n\pi \pm \frac{\pi }{2}$

C) $\theta =n\pi \pm {{(-1)}^{n}}\frac{\pi }{4}$

D) $\theta =2n\pi \pm \frac{\pi }{4}$

• A) $\varphi$

B) $\frac{\pi }{4}$

C) $\left\{ n\pi +\frac{\pi }{4}:n=1,\,2,\,3..... \right\}$

D) $\left\{ 2n\pi +\frac{\pi }{4}:n=1,\,2,\,3..... \right\}$

• A) $\theta =(6n+1)\pi /18,\,\forall n\in I$

B) $\theta =(6n+1)\pi /9,\,\forall n\in I$

C) $\theta =(3n+1)\pi /9,\,\forall n\in I$

D) None of these

• A) $k\pi ,k\in I$

B) $2k\pi ,k\in I$

C) $k\frac{\pi }{2},k\in I$

D) None of these

• A) $\frac{n\pi }{3}+\frac{\pi }{12}$

B) $\frac{n\pi }{3}+\frac{7\pi }{36}$

C) $n\pi +\frac{7\pi }{12}$

D) $n\pi +\frac{\pi }{12}$

• A) ${{30}^{o}},{{90}^{o}},{{150}^{o}}$

B) ${{60}^{o}},{{120}^{o}},{{180}^{o}}$

C) ${{0}^{o}},{{30}^{o}},{{150}^{o}}$

D) ${{45}^{o}},{{90}^{o}},{{135}^{o}}$

• A) One solution

B) Two solutions

C) Infinite number of solutions

D) No solutions

• A) 0

B) 1

C) 2

D) 3

• A) One solution

B) Two solutions

C) Infinite solutions

D) No solutions

• A) 0

B) 1

C) 2

D) 3

• A) $\frac{\pi }{6}$

B) $\frac{\pi }{12}$

C) $\frac{\pi }{3}$

D) $\frac{\pi }{4}$

• A) $\left[ 0,\,\frac{\pi }{2} \right]$

B) $\left[ -\frac{\pi }{2},\,0 \right]$

C) $\left[ \frac{\pi }{2},\,\pi \right]$

D) $\left[ \pi ,\frac{3\pi }{2} \right]$

• A) $\frac{\pi }{5},\frac{\pi }{5}$

B) $\frac{\pi }{5}$

C) $\frac{\pi }{4}$

D) None of these

• A) $-\frac{1}{2}\le \alpha \le \frac{1}{2}$

B) $-3\le \alpha \le 1$

C) $-\frac{3}{2}\le \alpha \le \frac{1}{2}$

D) $-1\le \alpha \le 1$

• A) Zero

B) Two

C) One

D) Infinite

• A) 0

B) 5

C) 6

D) 10

• A) Only one solution

B) Two solutions

C) Infinitely many solutions

D) No solution

• A) Finite solution

B) Infinite solution

C) One solution

D) No solution

• A) One solution

B) Two sets of solutions

C) Four sets of solutions

D) No solution

• A) ${{90}^{o}},{{60}^{o}},{{30}^{o}}$

B) ${{90}^{o}},{{150}^{o}},{{60}^{o}}$

C) ${{90}^{o}},{{45}^{o}},{{150}^{o}}$

D) ${{90}^{o}},{{30}^{o}},{{150}^{o}}$

• A) $\frac{\pi }{6},\frac{7\pi }{6}$

B) $\frac{\pi }{3},\frac{5\pi }{3}$

C) $\frac{\pi }{3},\frac{7\pi }{3}$

D) None of these

• A) ${{30}^{o}},{{45}^{o}}$

B) ${{45}^{o}},{{90}^{o}}$

C) ${{135}^{o}},{{150}^{o}}$

D) ${{30}^{o}},{{45}^{o}},{{90}^{o}},{{135}^{o}},{{150}^{o}}$

• A) ${{210}^{o}},{{300}^{o}}$

B) ${{240}^{o}},{{300}^{o}}$

C) ${{210}^{o}},{{240}^{o}}$

D) ${{210}^{o}},{{330}^{o}}$

• A) $\pm \frac{\pi }{6}$

B) $\pm \frac{\pi }{4}$

C) $\frac{3\pi }{2}$

D) None of these

• A) $\frac{\pi }{9},\frac{\pi }{4}$

B) $\frac{\pi }{3},\frac{\pi }{9}$

C) $\frac{\pi }{6},\frac{\pi }{9}$

D) $\frac{\pi }{3},\frac{\pi }{4}$

• A) $0\le x\le \frac{\pi }{2}$

B) $0\le x\le \pi$

C) For all $x\in R$

D) $x\ge 0$

• A) $\frac{\pi }{3}$

B) $\frac{\pi }{3},{{\cos }^{-1}}\frac{3}{5}$

C) ${{\cos }^{-1}}\frac{3}{5}$

D) $\frac{\pi }{3},\pi -{{\cos }^{-1}}\frac{3}{5}$

• A) ${{120}^{o}}$and ${{300}^{o}}$

B) ${{60}^{o}}$and ${{120}^{o}}$

C) ${{120}^{o}}$and ${{240}^{o}}$

D) ${{60}^{o}}$and ${{240}^{o}}$

• A) $\frac{\pi }{3}$

B) $\frac{\pi }{3},\frac{5\pi }{3}$

C) $\frac{\pi }{2},\frac{5\pi }{3},{{\cos }^{-1}}\left( -\frac{3}{2} \right)$

D) $\frac{5\pi }{3}$

• A) $\pi /6$

B) $\pi /2$

C) $\pi /4$

D) $3\pi /4$

• A) $-\frac{5\pi }{6}$

B) $-\frac{4\pi }{6}$

C) $\frac{4\pi }{6}$

D) $\frac{5\pi }{6}$

• A) $\theta ={{150}^{o}}$and ${{300}^{o}}$

B) $\theta ={{120}^{o}}$and ${{300}^{o}}$

C) $\theta ={{60}^{o}}$and ${{240}^{o}}$

D) $\theta ={{150}^{o}}$and ${{330}^{o}}$

• A) $\left( -\frac{\pi }{4},\frac{\pi }{4} \right)$

B) $\left( \frac{\pi }{4},\frac{3\pi }{4} \right)$

C) $\left( \frac{3\pi }{4},\frac{5\pi }{4} \right)$

D) $\left( \frac{5\pi }{4},\frac{7\pi }{4} \right)$

• A) No solution

B) One solution

C) Two solutions

D) Infinitely many solutions

• A) $n\pi +\frac{7\pi }{4}$

B) $n\pi +{{(-1)}^{n}}\frac{7\pi }{4}$

C) $2n\pi +\frac{7\pi }{4}$

D) None of these

• A) $n\pi +{{(-1)}^{n}}\frac{\pi }{6}$

B) $n\pi +\frac{\pi }{6}$

C) $2n\pi \pm \frac{\pi }{6}$

D) None of these

• A) $x=(2n-1)\frac{\pi }{2}$

B) $x=(2n+1)\frac{\pi }{4}$

C) $x=(2n+1)\frac{\pi }{3}$

D) None of these

• A) $\frac{\pi }{6},\frac{\pi }{3}$

B) $\frac{\pi }{6},\frac{5\pi }{6}$

C) $\frac{\pi }{3},\frac{\pi }{4}$

D) $\frac{\pi }{2},\pi$

• A) $2n\pi +\frac{\pi }{4}$

B) $(2n+1)\,\pi +\frac{\pi }{4}$

C) $n\pi +\frac{\pi }{4}$

D) $n\pi \pm \frac{\pi }{4}$

• A) ${{60}^{o}},\text{ }{{30}^{o}}$

B) ${{75}^{o}},\text{ }{{15}^{o}}$

C) ${{45}^{o}},\text{ }{{60}^{o}}$

D) ${{45}^{o}},\text{ }{{45}^{o}}$

• A) $\frac{5\pi }{6}$

B) $\frac{2\pi }{3}$

C) $\frac{\pi }{3}$

D) $\frac{\pi }{6}$

• A) ${{45}^{o}}$ and ${{60}^{o}}$

B) ${{45}^{o}}$and ${{90}^{o}}$

C) ${{45}^{o}}$only

D) ${{90}^{o}}$only

• A) $\frac{\pi }{3}$

B) $\frac{5\pi }{3}$

C) $\frac{2\pi }{3}$

D) $\frac{4\pi }{3}$

• A) $\frac{\pi }{3}$

B) $\frac{\pi }{4}$

C) $\frac{\pi }{2}$

D) None of these

• A) ${{100}^{o}}$and ${{260}^{o}}$

B) ${{80}^{o}}$and${{280}^{o}}$

C) ${{280}^{o}}$and ${{110}^{o}}$

D) ${{110}^{o}}$and ${{260}^{o}}$

• A) $\frac{5\pi }{4}$

B) $\frac{3\pi }{4}$

C) $\frac{\pi }{2}$

D) All values of x

• A) ${{30}^{o}}$

B) ${{45}^{o}}$

C) ${{60}^{o}}$

D) ${{75}^{o}}$

• A) $\frac{1}{2\sqrt{2}}$

B) $\frac{1}{\sqrt{2}}$

C) $\frac{1}{3\sqrt{2}}$

D) $\frac{1}{4\sqrt{2}}$

• A) $\frac{1}{\sqrt{2}}$

B) $\frac{1}{2}$

C) $\frac{1}{2\sqrt{2}}$

D) $\frac{\sqrt{3}}{2}$

• A) $\frac{7\pi }{24}$ or $\frac{11\pi }{24}$

B) $\frac{5\pi }{24}$

C) $\frac{\pi }{24}$

D) None of these

• A) $\sin \alpha$

B) $\cos \alpha$

C) $\sin \beta$

D) $\cos 2\beta$

• A) $x=2n\pi -\frac{\pi }{12}$ or $x=2n\pi +\frac{7\pi }{12}$

B) $x=n\pi \pm \frac{\pi }{12}$

C) $x=2n\pi +\frac{\pi }{12}$ or $x=2n\pi -\frac{7\pi }{12}$

D) $x=n\pi +\frac{\pi }{12}$ or $x=n\pi -\frac{7\pi }{12}$

• A) $n\pi$

B) $2n\pi +\frac{3\pi }{4}$

C) $2n\pi$

D) $(2n+1)\,\pi$

• A) $\frac{3}{5}$ or 1

B) $-\sin (B+2C)=\frac{1}{2}$ or $\frac{-2}{3}$

C) $\frac{4}{5}$ or $\frac{3}{4}$

D) $\pm \frac{1}{2}$