Question

If $\theta$ is any angle, then $se{c}^4\theta -se{c}^2\theta$ is equal to

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

Answer 1

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

${sec}^4\theta -{sec}^2\theta ={sec}^2\theta ({sec}^2\theta -1)=(1+{tan}^2\theta )\left({tan}^2\theta \right)[\because {sec}^2\theta =1+{tan}^2\theta ,\therefore {sec}^2\theta -1={tan}^2\theta ]={tan}^4\theta +{tan}^2\theta \left(Ans\right)$.