The value of (1-cos theta)(1+cos theta)(1+cot | vedclass

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Question

(A) Given expression: $(1-\cos 	heta)(1+\cos 	heta)(1+\cot^2 	heta)$ Using the identity $(1-x)(1+x) = 1-x^2$,we get: $(1-\cos^2 	heta)(1+\cot^2

Vedclass · Accepted Answer

$1$

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(A) Given expression: $(1-\cos 	heta)(1+\cos 	heta)(1+\cot^2 	heta)$ Using the identity $(1-x)(1+x) = 1-x^2$,we get: $(1-\cos^2 	heta)(1+\cot^2 	heta)$ Using the trigonometric identities $1-\cos^2 	heta = \sin^2 	heta$ and $1+\cot^2 	heta = \operatorname{cosec}^2 	heta$: $= \sin^2 	heta \cdot \operatorname{cosec}^2 	heta$ $= \sin^2 	heta \cdot \frac{1}{\sin^2 	heta} = 1$ Since the expression simplifies to $1$ regardless of the value of $	heta$ (provided $\sin 	heta 
eq 0$),for $	heta = \frac{\pi}{15}$,the value is $1$.

The value of $(1-\cos \theta)(1+\cos \theta)(1+\cot^2 \theta)$,when $\theta = \frac{\pi}{15}$ is

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