How to Prove tan^2(theta) +1=sec^2(theta)

 

Use the basic identity

$$\sin^2(\theta) + \cos^2(\theta) = 1$$

see: how to prove it

Divide both sides of the identity by $\cos^2(\theta)$

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

Final Answer:

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

This proves the identity.