Answer
$$\sin^2\alpha+\tan^2\alpha+\cos^2\alpha=\sec^2\alpha$$
The equation has been verified to be an identity.
Work Step by Step
$$\sin^2\alpha+\tan^2\alpha+\cos^2\alpha=\sec^2\alpha$$ $$(\sin^2\alpha+\cos^2\alpha)+\tan^2\alpha=\sec^2\alpha$$
Here we see on the left side, we have $\sin^2\alpha+\cos^2\alpha$, which is an identity and it equals $1$. Therefore, on the left side, $$(\sin^2\alpha+\cos^2\alpha)+\tan^2\alpha$$ $$=1+\tan^2\alpha$$ $$=\sec^2\alpha$$
Again, $1+\tan^2\alpha$ is also an identity and equals $\sec^2\alpha$
Hence, the identity has been proved.
