Question

Assertion :$\tan 3A-\tan 2A-\tan A=\tan 3A\tan 2A\tan A$ Reason: If $x=y+z$,then $\tan x-\tan y-\tan z=\tan x\tan y\tan z$

• 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. Assertion is false but Reason is true

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

Assertion:
$3A=A+2A\Rightarrow \tan 3A-\tan A-\tan 2A=\tan A\tan 2A\tan 3A$