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

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

anonymous · Answer

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

yamyam70 · Answer

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

anonymous · Answer

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

anonymous · Answer

$$
\cos x \sin x + 2 \cos^2 x - \sin x -2 \cos x = \cos x(\sin x+2\cos x)-\sin x -2\cos x
$$

anonymous · Answer

$$
=\cos x(\sin x +2\cos x)-(\sin x +2\cos x) = (\cos x -1)(\sin x +2\cos x)
$$

anonymous · Answer

The numerator and denominator cancel out.

anonymous · Answer

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

yamyam70 · Answer

I understand now, Thank you :)