Question

Assertion :Statement 1: General solution of $\frac{\tan 3x-\tan 1x}{1+\tan 3x\tan 1x}=1$ is $x=\frac{n\pi }{2}+\frac{\pi }{8},nϵI$ Reason: Statement 2: General solution of $\tan \alpha =1$ is $\alpha =n\pi +\frac{\pi }{4},nϵI.$

• A. Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1
• B. Both the statements are TRUE and STATEMENT 2 is NOT the correct explanation of STATEMENT 1
• C. STATEMENT 1 is TRUE and STATEMENT 2 is FALSE
• D. STATEMENT 1 is FALSE and STATEMENT 2 is TRUE

Answer 1

The correct option is A Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT 1

$\frac{\tan 3x-\tan 1x}{1+\tan 3x\tan 1x}=1$

or, $\tan (3x-x)=1$

or, $\tan 2x=1$---------------------1

Statement 2

$\tan \alpha =1=\tan \frac{\pi }{4}$

or, $\alpha =n\pi +\frac{\pi }{4}$ $n\in I$

$\therefore$ Statement 2 is correct.

From Statement 2, in Equation 1

$\tan 2x=\tan \frac{\pi }{4}$

or, $2x=n\pi +\frac{\pi }{4}$

or, $x=\frac{n\pi }{2}+\frac{\pi }{8}$

$\therefore$ Statement 1 is correct.