Question

Verify that (sinx -cosx)^2=1-2sin(x)cos(x)

Answer 1

(sinx - cosx)^2 = (sinx)^2 + (cosx)^2 - 2sinxcosx = 1-2sinxcosx

Answer 2

See below.

Explanation:

Left side = (sinx -cosx)^2 = sin^2 x + cos^2x - 2sinx cosx

Now sin^2 x + cos^2 x = 1 so we have:

1 - 2 sinx cosx = right side.