Question

If $\tan x-{\tan }^{2}x=1$, then the value of ${\tan }^{4}x-2{\tan }^{3}x-{\tan }^{2}x+2\tan x+1$ is:

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

We have, $\tan x-{\tan }^{2}x=1$..........(1)
Squaring both sides, we get,
${\tan }^{4}x-2{\tan }^{3}x+{\tan }^{2}x=1$
$\Rightarrow {\tan }^{4}x-2{\tan }^{3}x-{\tan }^{2}x+2\tan x=1+2\tan x-2{\tan }^{2}x$
$\therefore {\tan }^{4}x-2{\tan }^{3}x-{\tan }^{2}x+2\tan x+1=2+2(\tan x-{\tan }^{2}x)=1+2=4$ using (1)
Hence correct option is 'D'