(1 - cosx)(1 + cosx) = sin²x

Question

LHS: (1 - cosx)(1 + cosx)

= 1 - cos²x (find the rule)

= sin²x (find the rule)

(Algebra, Reciprocal, Quotient, Pythagorean, Odd/Even)

Answer 1

(a + b)(a – b) = a² – b² is an algebraic identity called difference of two squares

sin²x + cos²x = 1 is one of the Pythagorean identities in trigonometry

So

LHS: (1 - cosx)(1 + cosx)

= 1 - cos²x (Algebra)

= sin²x (Pythagorean)