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

Correct option is 3−1n+1π/6+nπ

Questions

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

The equation 1+sinx+....+sinnx+.....1−sinx+....+−1nsinnx+....=1−cos2x1+cos2x⇒1+sinx1−sinx=2sin2x2cos2x⇒1+sinx2cos2x=sin2xcos2x⇒1+sinx2=sin2x⇒1+2sinx=0⇒sinx=−12=sin-π6x=nπ+(−1)n+1π6

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

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