Question

Verify the Identity. PLease help :)


cos x sin x + 2 cos^2 x - sin x -2 cos x
____________________________________ = cos x -1
sin x + 2 cos x

Answer 1

in the numerator from first two take common cos x and from last two -1 and make factors.

Answer 2

is sine the common factor? is this factoring by grouping?

Answer 3

cosx (sin x+2 cos x)
similarly for second

Answer 4

\[
\cos x \sin x + 2 \cos^2 x - \sin x -2 \cos x = \cos x(\sin x+2\cos x)-\sin x -2\cos x
\]

Answer 5

\[
=\cos x(\sin x +2\cos x)-(\sin x +2\cos x) = (\cos x -1)(\sin x +2\cos x)
\]

Answer 6

The numerator and denominator cancel out.

Answer 7

This identity only holds true when: \[
\sin x +2\cos x \neq 0
\]

Answer 8

I understand now, Thank you :)