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

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Question

(B) Expand the given expression:
$(\sin x + cosecx)^2 = \sin ^2x + co\sec ^2x + 2\sin x \cdot cosecx = \sin ^2x + co\sec ^2x + 2$
$(cosx + \se

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(B) Expand the given expression:
$(\sin x + cosecx)^2 = \sin ^2x + co\sec ^2x + 2\sin x \cdot cosecx = \sin ^2x + co\sec ^2x + 2$
$(cosx + \sec x)^2 = cos^2x + \sec ^2x + 2cosx \cdot \sec x = cos^2x + \sec ^2x + 2$
$(	an x + \cot x)^2 = 	an ^2x + \cot ^2x + 2	an x \cdot \cot x = 	an ^2x + \cot ^2x + 2$
Substituting these into the expression:
$(\sin ^2x + cosec ^2x + 2) + (cos^2x + \sec ^2x + 2) - (	an ^2x + \cot ^2x + 2)$
$= (\sin ^2x + cos^2x) + cosec ^2x + \sec ^2x + 4 - 	an ^2x - \cot ^2x - 2$
$= 1 + (1 + \cot ^2x) + (1 + 	an ^2x) + 2 - 	an ^2x - \cot ^2x$
$= 1 + 1 + \cot ^2x + 1 + 	an ^2x + 2 - 	an ^2x - \cot ^2x$
$= 5$

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

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