11th Class Mathematics Trigonometric Identities Question Bank Critical Thinking

  • question_answer
    If \[\sin 6\theta =32{{\cos }^{5}}\theta \sin \theta -32{{\cos }^{3}}\theta \sin \theta +3x,\] then \[x=\] [EAMCET 2003]

    A) \[\cos \theta \]

    B) \[\cos 2\theta \]

    C) \[\sin \theta \]

    D) \[\sin 2\theta \]

    Correct Answer: D

    Solution :

    \[\sin 6\theta =2\sin 3\theta \cos 3\theta \] \[=2\,[3\sin \theta -4{{\sin }^{3}}\theta ]\,[4{{\cos }^{3}}\theta -3\cos \theta ]\] =24sinqcosq(sin2q+cos2q) -18sinqcosq - 32sin2qcos2q \[=32{{\cos }^{5}}\theta \sin \theta -32{{\cos }^{3}}\theta \sin \theta +3\sin 2\theta \] On comparing, \[x=\sin 2\theta .\]


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