If cos ^{2} theta-sin ^{2} theta=frac{1}{3}, | vedclass

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(A) We are given that $\cos ^{2} 	heta - \sin ^{2} 	heta = \frac{1}{3}$.....$(1)$We know the trigonometric identity $\cos ^{2} 	heta + \sin ^{2}

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$\frac{1}{3}$

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(A) We are given that $\cos ^{2} 	heta - \sin ^{2} 	heta = \frac{1}{3}$.....$(1)$We know the trigonometric identity $\cos ^{2} 	heta + \sin ^{2} 	heta = 1$.....$(2)$We need to find the value of $\cos ^{4} 	heta - \sin ^{4} 	heta$.Using the algebraic identity $a^{2} - b^{2} = (a - b)(a + b)$,we can write:$\cos ^{4} 	heta - \sin ^{4} 	heta = (\cos ^{2} 	heta - \sin ^{2} 	heta)(\cos ^{2} 	heta + \sin ^{2} 	heta)$Substituting the values from $(1)$ and $(2)$:$\cos ^{4} 	heta - \sin ^{4} 	heta = (\frac{1}{3}) 	imes (1)$$\cos ^{4} 	heta - \sin ^{4} 	heta = \frac{1}{3}$

If $\cos ^{2} \theta-\sin ^{2} \theta=\frac{1}{3},$ where $0 \leq \theta \leq \frac{\pi}{2},$ then the value of $\cos ^{4} \theta-\sin ^{4} \theta$ is

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