2 sin ^{2} theta+4 sec ^{2} theta+5 cot ^{2} | vedclass

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(D) Given expression: $2 \sin ^{2} 	heta+4 \sec ^{2} 	heta+5 \cot ^{2} 	heta+2 \cos ^{2} 	heta-4 	an ^{2} 	heta-5 \operatorname{cosec}^{2} 	het

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$1$

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(D) Given expression: $2 \sin ^{2} 	heta+4 \sec ^{2} 	heta+5 \cot ^{2} 	heta+2 \cos ^{2} 	heta-4 	an ^{2} 	heta-5 \operatorname{cosec}^{2} 	heta$Rearranging the terms based on trigonometric identities:$= 2(\sin ^{2} 	heta + \cos ^{2} 	heta) + 4(\sec ^{2} 	heta - 	an ^{2} 	heta) - 5(\operatorname{cosec}^{2} 	heta - \cot ^{2} 	heta)$Using the fundamental trigonometric identities:$1) \sin ^{2} 	heta + \cos ^{2} 	heta = 1$$2) \sec ^{2} 	heta - 	an ^{2} 	heta = 1$$3) \operatorname{cosec}^{2} 	heta - \cot ^{2} 	heta = 1$Substituting these values into the expression:$= 2(1) + 4(1) - 5(1)$$= 2 + 4 - 5$$= 1$

$2 \sin ^{2} \theta+4 \sec ^{2} \theta+5 \cot ^{2} \theta+2 \cos ^{2} \theta-4 \tan ^{2} \theta-5 \operatorname{cosec}^{2} \theta = \dots$

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