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.
