JEE Main & Advanced Mathematics Trigonometric Identities Question Bank Trigonometrical ratios of sum and difference of two and three angles

  • question_answer
    \[\frac{\cos 12{}^\circ -\sin 12{}^\circ }{\cos 12{}^\circ +\sin 12{}^\circ }+\frac{\sin 147{}^\circ }{\cos 147{}^\circ }=\] [MP PET 1991]

    A) 1

    B) -1

    C) 0

    D) None of these

    Correct Answer: C

    Solution :

    \[\frac{\cos \,{{12}^{o}}-\sin \,{{12}^{o}}}{\cos \,\,{{12}^{o}}+\sin \,\,{{12}^{o}}}+\frac{\sin \,\,{{147}^{o}}}{\cos \,\,{{147}^{o}}}\] \[=\frac{1-\tan \,\,{{12}^{o}}}{1+\tan \,\,{{12}^{o}}}+\tan \,\,{{147}^{o}}\]\[=\tan \,\,{{33}^{o}}-\tan \,\,{{33}^{o}}=0\].


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