JEE Main & Advanced Mathematics Trigonometric Identities Question Bank

done Numerical Value Type Questions - Trigonometric Ratios Total Questions - 15

• question_answer1)
  If \[{{\log }_{3}}\,\,\sin \,x-{{\log }_{3}}\,\,\cos x-{{\log }_{3}}\left( 1-\tan \,\,x \right)\]\[-{{\log }_{3}}\left( 1+\tan \,x \right)=-1,\] then find the value of \[\tan \,2x\].
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• question_answer2)
  If the value of \[\cos \frac{2\pi }{15}.\cos \frac{4\pi }{15}.cos\frac{8\pi }{15}.\cos \frac{14\pi }{15}\] is \[\frac{1}{k}\] then find k.
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• question_answer3)
  Find the maximum value of \[12\,\,\sin \theta -9\,\,{{\sin }^{2}}\theta .\]
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• question_answer4)
  Find total number of solutions of \[\sin \,\,x=\frac{|x|}{10}.\]
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• question_answer5)
  If \[\sin \theta +\text{cosec}\theta =2,\] then find the value of \[{{\sin }^{2}}\theta +\text{cose}{{\text{c}}^{2}}\theta .\]
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• question_answer6)
  If \[\alpha \] is the root of \[25\,{{\cos }^{2}}\theta +5\,\,\cos \theta -12=0,\] \[\pi /2<\alpha <\pi ,\] then find the value of \[\sin \,\,2\alpha \] is \[\frac{-k}{25}\] then find k.
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• question_answer7)
  If \[\theta \] lies in the second quadrant and \[3\tan \theta +4=0,\] then find the value of \[2\,\,\cot \theta -5\,\cos \theta +\sin \theta \] is \[\frac{6}{k}\] then find k.
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• question_answer8)
   Find the value of expression \[3\left[ {{\sin }^{4}}\left( \frac{\pi }{2}-\alpha  \right)+{{\sin }^{-1}}\left( 3\pi -\alpha  \right) \right]\]\[-2\left[ {{\cos }^{6}}\left( 3\frac{\pi }{2}+\alpha  \right)+{{\cos }^{6}}\left( 5\pi -\alpha  \right) \right]+6.\]
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• question_answer9)
  If \[\tan \left( \alpha +\beta  \right)=\frac{1}{2}\] and \[\tan \left( \alpha -\beta  \right)=\frac{1}{4},\] then find the value of \[\tan (2\alpha ).\]
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• question_answer10)
  If \[\frac{\sin \,3\theta +\sin 5\theta +\sin 7\theta +\sin 9\theta }{\cos 3\theta +\cos 5\theta +\cos 7\theta +\cos 9\theta }=\tan k\theta \] then find value of k.
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• question_answer11)
  Find the value of\[\frac{\cos 20{}^\circ +8\sin 70{}^\circ \sin 50{}^\circ \sin 10{}^\circ }{{{\sin }^{2}}80{}^\circ }.\]
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• question_answer12)
  If the value of \[\sin 20{}^\circ \,\,\sin \,40{}^\circ \,\,\sin \,\,60{}^\circ \,\,\sin 80{}^\circ \] is \[\frac{3}{k}\] then find k.
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• question_answer13)
  Find the value of  \[\cos 24{}^\circ +\cos 5{}^\circ +\cos 175{}^\circ +\cos 204{}^\circ +\cos \,\,300{}^\circ .\]
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• question_answer14)
   If \[3\,\,\sin \theta +5\cos \theta =5,\] then find the value of \[5\,\,\sin \theta -3\,\,\cos \,\,\theta .\]
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• question_answer15)
  Find the value of \[\cot x.\cot 2x-\cot 2x.\,\,\,\cot 3x-\cot 3x.\cot x.\]
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