Question

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

Answer 1

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

Answer 2

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

$⇒ \sin^4x = 1 – \sin^2x$

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

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

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

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