Question

(1-cos^2x)(1+tan^2x)=tan^2x

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the trigonometric identities

1 + tan²x = sec²x

1 - cos²x = sin²x and sec x = $\frac{1}{cosx}$

Consider the left side

(1 - cos²x)(1 + tan²x)

= sin²x × sec²x

= sin²x × $\frac{1}{cos^2x}$

= $\frac{sin^2x}{cos^2x}$

= tan²x