Math, asked by sasukesakura, 3 months ago

If sin^4 x + sin^2 x = 1. value of cot^4 x +cot^2 x

Answers

Answered by nithya12333
4

Step-by-step explanation:

sin4x + sin2x = 1 ⇒ sin4x = 1 – sin2x ⇒ sin4x = cos2x ...(i) ∴ cot4x + cot2x = cot2x (1 + cot2x) = cot2x . cosec2x = c o s 2 x s i n 2 x . s i n 2 x = c o s 2 x s i n 4 x =cos2xsin2x.sin2x=cos2xsin4x = = c o s 2 x c o s 2 x =cos2xcos2x = 1.

answer is 1

Answered by Anonymous
0

 \sin^4x +  \sin^2x = 1

 ⇒  \sin^4x = 1 –  \sin^2x

 \small{⇒  \sin {}^{4}x =  \cos {}^{2} x}

 \small{=  \cot^2x (1 +  \cot^2x) =  \cot^2x ×  \cosec^2x}

 =   \frac{ \cos {}^{2} x}{ \sin {}^{2}x \times \sin {}^{2}x}  =  \frac{ \cos {}^{2}x }{ \sin {}^{4} x}

=  \frac{ \cos {}^{2}x }{ \cos {}^{2} x}  = 1

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