Question

$se{c}^4\theta -se{c}^2\theta$ is equal to

• A. $ta{n}^2\theta -ta{n}^4\theta$
• B. $ta{n}^4\theta -ta{n}^2\theta$
• C. $ta{n}^4\theta +ta{n}^2\theta$
• D. $ta{n}^2\theta -ta{n}^4\theta$

Answer 1

The correct option is C $ta{n}^4\theta +ta{n}^2\theta$

$se{c}^4\theta -se{c}^2\theta =se{c}^2\theta (se{c}^2\theta -1)$
$=(1+ta{n}^2\theta )\left(ta{n}^2\theta \right)[\because se{c}^2\theta =1+ta{n}^2\theta ]$
$=ta{n}^4\theta +ta{n}^2\theta$