If (sin alpha + operatorname{cosec} alpha)^{2 | vedclass

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(B) Given expression: $(\sin \alpha + \operatorname{cosec} \alpha)^{2} + (\cos \alpha + \sec \alpha)^{2}$Expanding the squares using $(a+b)^{2} = a^{2

Vedclass · Accepted Answer

$7$

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(B) Given expression: $(\sin \alpha + \operatorname{cosec} \alpha)^{2} + (\cos \alpha + \sec \alpha)^{2}$Expanding the squares using $(a+b)^{2} = a^{2} + b^{2} + 2ab$:$= (\sin^{2} \alpha + \operatorname{cosec}^{2} \alpha + 2 \sin \alpha \operatorname{cosec} \alpha) + (\cos^{2} \alpha + \sec^{2} \alpha + 2 \cos \alpha \sec \alpha)$Since $\sin \alpha \operatorname{cosec} \alpha = 1$ and $\cos \alpha \sec \alpha = 1$:$= \sin^{2} \alpha + \operatorname{cosec}^{2} \alpha + 2 + \cos^{2} \alpha + \sec^{2} \alpha + 2$$= (\sin^{2} \alpha + \cos^{2} \alpha) + \operatorname{cosec}^{2} \alpha + \sec^{2} \alpha + 4$Using identities $\sin^{2} \alpha + \cos^{2} \alpha = 1$,$\operatorname{cosec}^{2} \alpha = 1 + \cot^{2} \alpha$,and $\sec^{2} \alpha = 1 + 	an^{2} \alpha$:$= 1 + (1 + \cot^{2} \alpha) + (1 + 	an^{2} \alpha) + 4$$= 7 + 	an^{2} \alpha + \cot^{2} \alpha$Comparing this with $K + 	an^{2} \alpha + \cot^{2} \alpha$,we get $K = 7$.

If $(\sin \alpha + \operatorname{cosec} \alpha)^{2} + (\cos \alpha + \sec \alpha)^{2} = K + \tan^{2} \alpha + \cot^{2} \alpha$,then the value of $K$ is

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