frac{2sin theta tan theta (1 - tan theta ) + | vedclass

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(B) Given expression: $E = \frac{2\sin 	heta 	an 	heta (1 - 	an 	heta ) + 2\sin 	heta \sec^2 	heta}{(1 + 	an 	heta )^2}$Factor out $2\sin 	h

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$\frac{2\sin 	heta}{1 + 	an 	heta}$

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(B) Given expression: $E = \frac{2\sin 	heta 	an 	heta (1 - 	an 	heta ) + 2\sin 	heta \sec^2 	heta}{(1 + 	an 	heta )^2}$Factor out $2\sin 	heta$ from the numerator:$E = \frac{2\sin 	heta [	an 	heta (1 - 	an 	heta ) + \sec^2 	heta]}{(1 + 	an 	heta )^2}$Expand the terms inside the bracket:$E = \frac{2\sin 	heta [	an 	heta - 	an^2 	heta + \sec^2 	heta]}{(1 + 	an 	heta )^2}$Use the trigonometric identity $1 + 	an^2 	heta = \sec^2 	heta$,which implies $\sec^2 	heta - 	an^2 	heta = 1$:$E = \frac{2\sin 	heta [	an 	heta + 1]}{(1 + 	an 	heta )^2}$Cancel the common term $(1 + 	an 	heta)$:$E = \frac{2\sin 	heta}{1 + 	an 	heta}$.

$\frac{2\sin \theta \tan \theta (1 - \tan \theta ) + 2\sin \theta \sec^2 \theta}{(1 + \tan \theta )^2} = $

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