3 tan-1a is equal to

Question

3 tan-1a is equal to (A)  tan(3a+a3/1+3a2) (B)  tan-1(3a-a3/1+3a2) (C)  tan-1(3a+a3/1-3a2) (D)  tan-1(3a-a3/1-3a2)

Tardigrade Admin · Accepted Answer

We know that tan 3A =( 3 tan A-tan3A/1-3 tan2A) ∴ 3 A = tan-1 (3 tan A-tan3A/1-3tan2A) Put tan A = a i.e., A = tan-1a ∴ 3tan-1 a = tan-1 (3a-a3/1-3a2)

Q. $3 tan^{- 1} a$ is equal to

$tan \frac{3 a + a ^{3}}{1 + 3 a ^{2}}$

$tan^{- 1} \frac{3 a - a ^{3}}{1 + 3 a ^{2}}$

$tan^{- 1} \frac{3 a + a ^{3}}{1 - 3 a ^{2}}$

$tan^{- 1} \frac{3 a - a ^{3}}{1 - 3 a ^{2}}$

We know that
$t an 3 A = \frac{3 t an A - t a n ^{3} A}{1 - 3 t a n ^{2} A}$
$∴ 3 A = t a n^{- 1} \frac{3 t an A - t a n ^{3} A}{1 - 3 t a n ^{2} A}$
Put $t an A = a$ i.e., $A = t a n^{- 1} a$
$∴ 3 t a n^{- 1} a = t a n^{- 1} \frac{3 a - a ^{3}}{1 - 3 a ^{2}}$

Q. 3tan−1a is equal to

tan1+3a23a+a3​

tan−11+3a23a−a3​

tan−11−3a23a+a3​

tan−11−3a23a−a3​