Prove: 2sin^-1 (3/5) – tan^-1 (17/31) = π/4 2tan^-1 (1/5) + tan^-1 (1/8) = tan^-1 (4/7)

Question

Prove:

(i) 2sin^-1 (3/5) – tan^-1 (17/31) = π/4

(ii) 2tan^-1 (1/5) + tan^-1 (1/8) = tan^-1 (4/7)

Answer 1

(i) Given as 2sin^-1(3/5) – tan^-1(17/31) = π/4

Considering L.H.S.

= 2 sin^-1(3/5) - tan^-1(17/31)

As we know that

On, substituting this formula

Therefore, 2sin-1(3/5) - tan-1(17/31) = π/4

Hence, proved

(ii) Given as 2tan^-1(1/5) + tan^-1(1/8) = tan^-1(4/7)

Considering L.H.S.

= 2tan^-1(1/5) + tan^-1(1/8)

As we know that

From formula

Hence, proved