Question

sin⁻¹ 3/5 + tan⁻¹ 1/7 is......,Select Proper option from the given options.
(a) π/4
(b) π/5
(c) π
(d) sin⁻¹ 4/5

Answer 1

we have to find the value of sin^-1(3/5) + tan^-1(1/7)

Let sin^-1(3/5) = A
sinA = 3/5 => tanA = 3/4 .......(1)

similarly, tan^-1(1/7) = B
tanB = 1/7 .........................(2)

sin^-1(3/5) + tan^-1(1/7) = tan^-1(3/4) + tan^-1(1/7)

we know, tan^-1x + tan^-1y = tan^-1[(x +y)/(1 - xy)]

so, tan^-1(3/4) + tan^-1(1/7) = tan^-1[ (3/4 + 1/7)/(1 - 3/4 × 1/7)]

= tan^-1[(21 + 4)/(28 - 3)]

= tan^-1[25/25]

= tan^-1(1) = π/4

hence, option (a) is correct.