simplify (sinx - cosx) (sinx + cosx)
[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)
Answer:
Formula used:
\(→( \sin(x) - \cos(x))( \sin(x) + \cos(x)) \\ = { \sin }^{2}(x) - \cos^{2} (x) \\ = - ( { \cos }^{2}(x) - { \sin }^{2} (x)) \\ = \boxed{ - \cos(2x) }✓\)
