verify tan^2x=sec^2x

Question

 Tan^2X+1=Sec^2X

Answer 1

tan²(x) + 1 = sec²(x)

 

Use the following identities:

• tan(x) = sin(x)/cos(x)
• sec(x) = 1/cos(x)

 

sin²(x)/cos²(x) + 1 = 1/cos²(x)

 

Multiply both sides by cos²(x):

 

sin²(x) + cos²(x) = 1

 

This is the Pythagorean Identity.