Question

Assertion :$\tan 5\theta -\tan 3\theta -\tan 2\theta =\tan 5\theta \tan 3\theta \tan 2\theta$ Reason: $x=y+z\Rightarrow \tan x-\tan y-\tan z=\tan x\tan y\tan z$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Reason is true as

$x=y+z$

$\Rightarrow \tan x=\tan (y+z)=\frac{\tan y+\tan z}{1-\tan y\tan z}$

$\Rightarrow \tan x-\tan x\tan y\tan x=\tan y+\tan z$

$\Rightarrow \tan x-\tan y-\tan z=\tan x\tan y\tan z$

As $5\theta =3\theta +2\theta$ using reason

We get $\tan 5\theta -\tan 3\theta -\tan 2\theta =\tan 5\theta \tan 3\theta \tan 2\theta$

Hence assertion is true.