The general solution of the equation $$1$$−$$sinx+$$....$$+$$−$$1nsinnx+$$...$$.1+sinx+$$....$$+sinnx+$$.....$$=1$$−$$cos2x1+cos2x$$ , x≠$$2n+1$$π$$/2$$,n∈I is

Correct option is 2−1nπ/6+nπ

Questions

The general solution of the equation $\frac{1 - \sin x + .... + {(- 1)}^{n} \sin^{n} x + ....}{1 + \sin x + .... + \sin^{n} x + .....} = \frac{1 - \cos 2 x}{1 + \cos 2 x}$ , $x \neq (2 n + 1) π / 2, n \in I$ is

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−1nπ/3+nπ

−1nπ/6+nπ

−1n+1π/6+nπ

−1n−1π/3+nπ

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detailed solution

Correct option is B

We have 1−sinx+....+−1nsinnx+....1+sinx+....+sinnx+.....=1−cos2x1+cos2xNumerator and denominator both are in GP S∞=a1-r⇒11+sinx×1−sinx1=2sin2x2cos2x,∵−1

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The general solution of the equation 1−sinx+....+−1nsinnx+....1+sinx+....+sinnx+.....=1−cos2x1+cos2x , x≠2n+1π/2,n∈I is

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The general solution of the equation $\frac{1 - \sin x + .... + {(- 1)}^{n} \sin^{n} x + ....}{1 + \sin x + .... + \sin^{n} x + .....} = \frac{1 - \cos 2 x}{1 + \cos 2 x}$ , $x \neq (2 n + 1) π / 2, n \in I$ is