Question

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

Answer 1

Answer:

D

Step-by-step explanation:

First simplify given expression:

$(1-\sin ^2x)\cdot \tan (-x)=\cos^2x\cdot (-\tan x)=-\cos^2x\cdot \dfrac{\sin x}{\cos x}=-\cos x\sin x.$

Now consider all options:

A. True

$(1-\cos^2 x)\cdot \cot (-x)=\sin^2 x\cdot (-\cot x)=-\sin^2 x\cdot \dfrac{\cos x}{\sin x}=-\sin x\cos x=-\cos x\sin x.$

B. True

$(\cos^2 x-1)\cdot \cot x=-\sin^2 x\cdot \cot x=-\sin^2 x\cdot \dfrac{\cos x}{\sin x}=-\sin x\cos x=-\cos x\sin x.$

C. True

$(\sin ^2x-1)\cdot \tan x=-\cos^2x\cdot \tan x=-\cos^2x\cdot \dfrac{\sin x}{\cos x}=-\cos x\sin x.$

D. False

$(\cos^2 x-1)\cdot \cot (-x)=(-\sin^2 x)\cdot (-\cot x)=\sin^2 x\cdot \dfrac{\cos x}{\sin x}=\sin x\cos x=\cos x\sin x.$