Question

The value of $\tan 3A-\tan 2A-\tan A$ is

• A. $\tan 3A\tan 2A\tan A$
• B. $-\tan 3A\tan 2A\tan A$
• C. $\tan A\tan 2A-\tan 2A\tan 3A-\mathrm{tanA}$
• D. None of there

Answer 1

Answer: (A)

$\tan 3A\tan 2A\tan A$

$tan3A-tan2A-tanA$

Let us suppose that, $tan3A-tan2A-tanA=K$

then, $tan3A.k+tan2A+tanA...\left(1\right)$

we know that

$tan(A+B)=\frac{tanA+tanB}{1-tanA+tanB}$

$tan(A+B)(1-tanA+tan+B)=tanA+tanB...\left(2\right)$

from (1) & (2)

$tan3A=k+tan2A+tanA(1-tan2AtanA)$

$tan3A=k+tan3A(1-tan2AtanA)$

$tan3A=k+tan3A-tan3A..tan2A.tanA$

$o=k-tan3A.tan2A.tanA$

$\therefore k=tan3A.tan2A.tanA$

$\therefore tan3A-tan2A-tanA=tan3A.tan2A.tanA$

$\therefore$ So,the answer is 'A $tan3A.tan2aA.TanA$