The value of the expression (sinx + cosecx)^2 | vedclass

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(B) Let the expression be $E = (\sin x + \csc x)^2 + (\cos x + \sec x)^2 - (	an x + \cot x)^2$.Expanding the squares using $(a+b)^2 = a^2 + b^2 + 2ab

Vedclass · Accepted Answer

$5$

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(B) Let the expression be $E = (\sin x + \csc x)^2 + (\cos x + \sec x)^2 - (	an x + \cot x)^2$.Expanding the squares using $(a+b)^2 = a^2 + b^2 + 2ab$:$E = (\sin^2 x + \csc^2 x + 2 \sin x \csc x) + (\cos^2 x + \sec^2 x + 2 \cos x \sec x) - (	an^2 x + \cot^2 x + 2 	an x \cot x)$.Since $\sin x \csc x = 1$,$\cos x \sec x = 1$,and $	an x \cot x = 1$:$E = (\sin^2 x + \cos^2 x) + \csc^2 x + \sec^2 x + 2 + 2 - (	an^2 x + \cot^2 x + 2)$.Using the identity $\sin^2 x + \cos^2 x = 1$:$E = 1 + \csc^2 x + \sec^2 x + 4 - 	an^2 x - \cot^2 x - 2$.$E = 3 + (\csc^2 x - \cot^2 x) + (\sec^2 x - 	an^2 x)$.Using the identities $\csc^2 x - \cot^2 x = 1$ and $\sec^2 x - 	an^2 x = 1$:$E = 3 + 1 + 1 = 5$.

The value of the expression $(sinx + cosecx)^2 + (cosx + secx)^2 - (tanx + cotx)^2$ wherever defined is equal to

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