Question

Simplify (sinx - cosx) (sinx + cosx)

Answer 1

Formula used:

• (a-b)(a+b) = a²-b²
• cos²(x)-sin²(x) = cos(2x)

`→( \sin(x) - \cos(x))( \sin(x) + \cos(x)) \\ = { \sin }^(2)(x) - \cos^(2) (x) \\ = - ( { \cos }^(2)(x) - { \sin }^(2) (x)) \\ = \boxed{ - \cos(2x) }✓`

• -cos(2x) is the right answer.

Answer 2

[sin(x) - cos(x)][sin(x) + cos(x)]
sin(x)[sin(x) + cos(x)] - cos(x)[sin(x) + cos(x)]
sin(x)[sin(x)] + sin(x)[cos(x)] - cos(x)[sin(x)] - cos(x)[cos(x)]
sin²(x) + sin(x)cos(x) - sin(x)cos(x) - cos²(x)
sin²(x) - cos²(x)
-cos(2x)