JEE Main & Advanced Mathematics Inverse Trigonometric Functions Question Bank

done Numerical Value Type Questions - Inverse Trigonometric Function Total Questions - 15

• question_answer1)
  If the value of \[\cot \,\left( \sum\limits_{n=1}^{19}{{{\cot }^{-1}}\left( 1+\sum\limits_{p=1}^{n}{2p} \right)} \right)\] is \[\frac{m}{n},\] then \[m+n\] is
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• question_answer2)
  The value of \[\sin \left( 2{{\tan }^{-1}}\frac{1}{3} \right)+\cos \left( {{\tan }^{-1}}2\sqrt{2} \right)\]is \[\frac{p}{q},\] then \[pq\] is
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• question_answer3)
  If \[{{\cos }^{-1}}\left( \frac{2}{3x} \right)+{{\cos }^{-1}}\left( \frac{3}{4x} \right)=\frac{\pi }{2}\left( x>\frac{3}{4} \right)\] and x is equal to \[\frac{\sqrt{p}}{q},\] then \[p-q\] is
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• question_answer4)
  If \[si{{n}^{-1}}x+{{\sin }^{-1}}y+{{\sin }^{-1}}z=\frac{3\pi }{2}\] then the value of \[{{x}^{100}}+{{y}^{100}}+{{z}^{100}}-\frac{3}{{{x}^{101}}+{{y}^{101}}+{{z}^{101}}}\] is
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• question_answer5)
  If a and b are the roots of the equation \[{{x}^{2}}-4x+1=0\] \[(a>b)\]then the value of \[f(\alpha ,\beta )=\frac{{{\beta }^{3}}}{2}\cos e{{c}^{2}}\,\left( \frac{1}{2}{{\tan }^{-1}}\frac{\beta }{\alpha } \right)+\frac{{{\alpha }^{3}}}{2}{{\sec }^{2}}\left( \frac{1}{2}{{\tan }^{-1}}\frac{\alpha }{\beta } \right)\]is
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• question_answer6)
  The value of \[{{\cos }^{-1}}\left( \cos \frac{5\pi }{3} \right)+{{\sin }^{-1}}\left( \sin \frac{5\pi }{3} \right)\] is
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• question_answer7)
  \[\cos \left[ {{\cos }^{-1}}\left( \frac{-1}{7} \right)+{{\sin }^{-1}}\left( \frac{-1}{7} \right) \right]=\]
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• question_answer8)
  If \[4{{\sin }^{-1}}x+{{\cos }^{-1}}x=\pi ,\] then x is equal to
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• question_answer9)
  If \[\alpha ={{\cos }^{-1}}\left( \frac{3}{5} \right),\] \[\beta ={{\tan }^{-1}}\left( \frac{1}{3} \right),\] where \[0<\alpha ,\beta <\frac{\pi }{2},\] and \[\alpha -\beta \] is equal to \[{{\cos }^{-1}}\left( \frac{a}{b\sqrt{c}} \right),\] then \[a+bc\] is
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• question_answer10)
  The value of x which satisfies the equation \[{{\tan }^{-1}}x={{\sin }^{-1}}\left( \frac{3}{\sqrt{10}} \right)\] is
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• question_answer11)
  If \[{{\sin }^{-1}}\left( \frac{x}{5} \right)+\cos e{{c}^{-1}}\left( \frac{5}{4} \right)=\frac{\pi }{2},\] then the value of x is
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• question_answer12)
  If \[{{\cos }^{-1}}\sqrt{p}+{{\cos }^{-1}}\sqrt{1-p}+{{\cos }^{-1}}\sqrt{1-q}=\frac{3\pi }{4}\] then the value of q is equal to
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• question_answer13)
  Number of solutions of the equation \[{{\tan }^{-1}}(1+x)+{{\tan }^{-1}}(1-x)=\frac{\pi }{2}\] are
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• question_answer14)
  If \[{{\tan }^{-1}}(2x)+{{\tan }^{-1}}(3x)=\frac{\pi }{4}\] then the number of solutions are
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• question_answer15)
  If \[\angle A=90{}^\circ \] in the triangle ABC, then \[{{\tan }^{-1}}\left( \frac{c}{a+b} \right)+{{\tan }^{-1}}\left( \frac{b}{a+c} \right)=\frac{\pi }{k},\] then the value of k is
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