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If sin4x + sin2x = 1 then what is 1 are the value of cot4x + cot2x?(a) cos2x (b) sin2x (c) tan2x (d) 1 |
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Answer» (d) 1 sin4x + sin2x = 1 ⇒ sin4x = 1 – sin2x ⇒ sin4x = cos2x ...(i) ∴ cot4x + cot2x = 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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