11th Class Mathematics Trigonometric Identities Question Bank Critical Thinking

  • question_answer \[{{\left( \frac{\cos A+\cos B}{\sin A-\sin B} \right)}^{n}}+{{\left( \frac{\sin A+\sin B}{\cos A-\cos B} \right)}^{n}}\](n even or odd) =

    A) \[2{{\tan }^{n}}\frac{A-B}{2}\]

    B) \[2{{\cot }^{n}}\frac{A-B}{2}\]

    C) \[0\]

    D) None of these

    Correct Answer: B

    Solution :

     The expression reduces to \[{{\cot }^{n}}\frac{A-B}{2}+{{\cot }^{n}}\frac{B-A}{2}\] If n is even, answer is (b) and if n is odd answer is (c).

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