Question

Prove the identity and include the rule

Answer 1

Hi there!

To begin, we can distribute sec²x with (1 - sin²x):

= sec²x - sec²xsin²x

Which simplifies to:

= sec²x - tan²x

Recall the Pythagorean identity:

1 + tan²x = sec²x

Rearrange alike to the solved for expression above:

1 = sec²x - tan²x

Thus, using the Pythagorean Identity, sec²x(1 - sin²x) = 1.