Answer:
see explanation
Explanation:
using the trigonometric identity
sin²x + cos²x = 1 ( subtract cos²x from both sides ) , so
sin²x = 1 - cos²x → (1)
consider the left side
(sinx - cosx)(sinx + cosx) ← expand using FOIL
= sin²x + sinxcosx - sinxcosx - cos²x ← collect like terms
= sin²x - cos²x ← substitute (1) from above into the expression
= (1 - cos²x) - cos²x
= 1 - cos²x - cos²x
= 1 - 2cos²x
= right side , thus verified