Simplify: (csc x-tan x) sin x cos x=
A) $\sin x-\cos ^{2} x$
B) $\cos x-\sin ^{2} x$
C) $\sin ^{2} x+\cos x$
D) $\cos ^{2} x-\sin x$

Question

Simplify:  (csc x-tan x) sin x cos x= 
A) $\sin x-\cos ^{2} x$
B) $\cos x-\sin ^{2} x$
C) $\sin ^{2} x+\cos x$
D) $\cos ^{2} x-\sin x$

Quizplus · Accepted Answer

The expression simplifies to $\cos x - \sin^2 x$. This is because $\csc x = \frac{1}{\sin x}$ and $\tan x = \frac{\sin x}{\cos x}$. Substituting these into the original expression gives $(\frac{1}{\sin x} - \frac{\sin x}{\cos x})\sin x \cos x$, which simplifies to $\cos x - \sin^2 x$.

Simplify: (Csc X-Tan X) Sin X Cos X= sin⁡x−cos⁡2x\sin x-\cos ^{2} xsinx−cos2x

Simplify: (Csc X-Tan X) Sin X Cos X= $\sin x-\cos ^{2} x$