Question

sec^2 theta - cos^2 theta = sin^2 theta (sec^2 theta +1)

Answer 1

Hey check your answer

Answer 2

Proved that $\sec^{2}\theta - \cos^{2}\theta = \sin^{2}\theta(\sec^{2}\theta + 1 )$

Step-by-step explanation:

We have to prove that $\sec^{2}\theta - \cos^{2}\theta = \sin^{2}\theta(\sec^{2}\theta + 1 )$

Now, left hand side

= $\sec^{2}\theta - \cos^{2}\theta$

= $1 + \tan^{2}\theta + \sin^{2}\theta - 1$

{Since, we know that $\sec^{2}\theta - \tan^{2}\theta = 1$ and $\sin^{2}\theta + \cos^{2}\theta = 1$}

= $\tan^{2}\theta + \sin^{2}\theta$

= $\frac{\sin^{2}\theta }{\cos^{2}\theta} + \sin^{2}\theta$

= $\sin^{2}\theta[\frac{1}{\cos^{2}\theta} + 1 ]$

= $\sin^{2}\theta(\sec^{2}\theta + 1 )$

= right hand side.

Hence, it proved.