What is the value of (1+cot A)^{2}+(1-cot A)^ | vedclass

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(A) Given expression: $(1+\cot A)^{2}+(1-\cot A)^{2}$Expand the squares using the identities $(a+b)^{2} = a^{2}+b^{2}+2ab$ and $(a-b)^{2} = a^{2}+b^{2

Vedclass · Accepted Answer

$2 \operatorname{cosec}^{2} A$

Vedclass · Answer

(A) Given expression: $(1+\cot A)^{2}+(1-\cot A)^{2}$Expand the squares using the identities $(a+b)^{2} = a^{2}+b^{2}+2ab$ and $(a-b)^{2} = a^{2}+b^{2}-2ab$:$= (1 + \cot^{2} A + 2 \cot A) + (1 + \cot^{2} A - 2 \cot A)$Combine like terms:$= 1 + \cot^{2} A + 2 \cot A + 1 + \cot^{2} A - 2 \cot A$$= 2 + 2 \cot^{2} A$Factor out $2$:$= 2(1 + \cot^{2} A)$Using the trigonometric identity $1 + \cot^{2} A = \operatorname{cosec}^{2} A$:$= 2 \operatorname{cosec}^{2} A$

What is the value of $(1+\cot A)^{2}+(1-\cot A)^{2}$?

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