Question

The expression _______ is not equivalent to (1 − sin2(x)) tan(-x).

a. (1 - cos^2(x)) cot(-x)
b. (cos^2(x) - 1) cot(x)
c. (sin^(x) - 1) tan(x)
d. (cos^2(x) - 1) cot(-x)

Answer 1

d. (cos^2(x) - 1) cot(-x)

Explanation:

Answer 2

D

Explanation:

First simplify given expression:

`(1-\sin ^2x)\cdot \tan (-x)=\cos^2x\cdot (-\tan x)=-\cos^2x\cdot (\sin x)/(\cos x)=-\cos x\sin x.`

Now consider all options:

A. True

`(1-\cos^2 x)\cdot \cot (-x)=\sin^2 x\cdot (-\cot x)=-\sin^2 x\cdot (\cos x)/(\sin x)=-\sin x\cos x=-\cos x\sin x.`

B. True

`(\cos^2 x-1)\cdot \cot x=-\sin^2 x\cdot \cot x=-\sin^2 x\cdot (\cos x)/(\sin x)=-\sin x\cos x=-\cos x\sin x.`

C. True

`(\sin ^2x-1)\cdot \tan x=-\cos^2x\cdot \tan x=-\cos^2x\cdot (\sin x)/(\cos x)=-\cos x\sin x.`

D. False

`(\cos^2 x-1)\cdot \cot (-x)=(-\sin^2 x)\cdot (-\cot x)=\sin^2 x\cdot (\cos x)/(\sin x)=\sin x\cos x=\cos x\sin x.`