Question

PT----Sec^4 theta - sec^2 theta = 1-cos theta/1+cos theta

Answer 1

Answer:

$sec^4\theta-sec^2\theta=\frac{2(1-cos2\theta)}{(1+cos2\theta)^2}$

Step-by-step explanation:

The identity

$Sec^4\theta - sec^2\theta = \frac{1-cos\theta}{1+cos\theta}$ does not hold for $\theta=\frac{\pi}{4}$

I think your question may be

$sec^4\theta-sec^2\theta=\frac{2(1-cos2\theta)}{(1+cos2\theta)^2}$

Formula used:

$cos2A=2\:cos^2A-1\\\\cos2A=\frac{1-tan^2A}{1+tan^2A}$

Now,

$sec^4\theta-sec^2\theta\\\\=sec^2\theta(sec^2\theta-1)\\\\=sec^2\theta.tan^2\theta\\\\=\frac{tan^2\theta}{cos^2\theta}\\\\=\frac{\frac{1-cos2\theta}{1+cos2\theta}}{\frac{1+cos2\theta}{2}}\\\\=\frac{2(1-cos2\theta)}{(1+cos2\theta)^2}$