JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Application +4 | -1

The expression

\left(\frac{\cos \mathrm{A}+\cos \mathrm{B}}{\sin \mathrm{A}-\sin \mathrm{B}}\right)^{\mathrm{n}}+\left(\frac{\sin \mathrm{A}+\sin \mathrm{B}}{\cos \mathrm{A}-\cos \mathrm{B}}\right)^{\mathrm{n}}=

View answer and explanation

Correct option: A

2 \cot ^{\mathrm{n}}\left(\frac{\mathrm{A}-\mathrm{B}}{2}\right)

\mathrm{n}

is even

Option A is correct because the expression simplifies to a trigonometric form, and the result depends on whether n is even or odd.

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