Question

(1 + cot² A) + (1 + tan² A) is equal to ______.

Options

• \[\frac{1}{\sin^2 A - \cos^2 A}\]

• sec² A − cosec² A

• sin² A − sin⁴ A

• sec² A . cosec² A

Answer 1

(1 + cot² A) + (1 + tan² A) is equal to sec² A . cosec² A.

Explanation:

Solving,

\[\Rightarrow (1 + \cot^2 A) + (1 + \tan^2 A)\]

\[\Rightarrow \operatorname{cosec}^2 A + \sec^2 A\]

\[\Rightarrow \frac{1}{\sin^2 A} + \frac{1}{\cos^2 A}\]

\[\Rightarrow \frac{\cos^2 A + \sin^2 A}{\sin^2 A \cdot \cos^2 A}\]

Substituting, \[\sin^2 A + \cos^2 A = 1\], we get:

\[\Rightarrow \frac{1}{\sin^2 A \cdot \cos^2 A}\]

\[\Rightarrow \operatorname{cosec}^2 A \cdot \sec^2 A\]