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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 $(1+\cot A)^{2}+(1-\cot A)^{2}$?

Similar Questions

If $\sin \beta$ is the geometric mean between $\sin \alpha$ and $\cos \alpha,$ then $\cos 2\beta$ is equal to

The value of $\tan 1^{\circ} \tan 2^{\circ} \ldots \tan 89^{\circ}$ is

If $\sin A = n \sin B,$ then $\frac{n - 1}{n + 1} \tan \frac{A + B}{2} = $

$\tan 15^\circ = $

The value of $\sin^2 \frac{\pi}{8} + \sin^2 \frac{3\pi}{8} + \sin^2 \frac{5\pi}{8} + \sin^2 \frac{7\pi}{8}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module