1.

If sin4x + sin2x = 1 then what is 1 are the value of cot4x + cot2x?(a) cos2x (b) sin2x (c) tan2x (d) 1

Answer»

(d) 1

sin4x + sin2x = 1 

⇒ sin4x = 1 – sin2

⇒ sin4x = cos2x              ...(i) 

∴ cot4x + cot2

= cot2x (1 + cot2x) = cot2x . cosec2x

\(=\frac{cos^2\,x}{sin^2\,x.sin^2\,x}=\frac{cos^2\,x}{sin^4\,x}\)

\(=\frac{cos^2\,x}{cos^2\,x}\) = 1.                       [Using (i)]



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