If $\smallint \,\,\frac{{{{\sin }^8}\,\,x\,\, - \,\,{{\cos }^8}\,\,x}}{{1 - 2\,\,{{\sin }^2}\,\,x\;\,\,{{\cos }^2}\,\,x}}\,\,\;dx = A\,\,\sin \,\,\,2x + B$, then

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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\int \,\,\frac{{{{\sin }^8}\,\,x\,\, - \,\,{{\cos }^8}\,\,x}}{{1 - 2\,\,{{\sin }^2}\,\,x\;\,\,{{\cos }^2}\,\,x}}\,\,\;dx = A\,\,\sin \,\,\,2x + B

, then

View answer and explanation

Correct option: A

A = - \,\,\frac{1}{2}

Option A is correct because after simplifying the integral, the coefficient of

\sin \,2x

- \,\frac{1}{2}