Question

(1 + tan² A) × cos² A − 1 is ______.

Options

• 1

• −2

• 0

• 2

Answer 1

(1 + tan² A) × cos² A − 1 is 0.

Explanation:

Solving,

\[\Rightarrow (1 + \tan^2 A) \times \cos^2 A - 1\]

\[\Rightarrow \left(1 + \frac{\sin^2 A}{\cos^2 A}\right) \times \cos^2 A - 1\]

\[\Rightarrow \left(\frac{\cos^2 A + \sin^2 A}{\cos^2 A}\right) \times \cos^2 A - 1\]

\[\Rightarrow \frac{1}{\cos^2 A} \times \cos^2 A - 1\]

\[\Rightarrow 1 - 1\]

\[\Rightarrow 0.\]