Question

Simplify :
4(1 – $si{n}^2\theta$) (1 + $ta{n}^2\theta$)

• A. 4
• B. 1
• C. 2
• D. 0

Answer 1

The correct option is A

4

Using the identity,
1 - $si{n}^2\theta$ = $co{s}^2\theta$ and
1 + $ta{n}^2\theta$ = $se{c}^2\theta$

We have, 4(1 – $si{n}^2\theta$) (1 + $ta{n}^2\theta$)
$=4co{s}^2\theta \times se{c}^2\theta =4(\because sec\theta =\frac{1}{cos\theta })$