Question

Then value of tan(cos⁻¹ 3/4+sin⁻¹3/4-sec⁻¹ 3) is......,Select Proper option from the given options.
(a) 1/√2
(b) 1/√3
(c) 1/2√3
(d) 1/2√2

Answer 1

we have to find the value of tan[cos^-1(3/4) + sin^-1(3/4) - sec^-1(3) ]

we know , sin^-1x + cos^-1x = π/2 , for all x belongs to 0 ≤ x ≤ 1
so, cos^-1(3/4) + sin^-1(3/4) = π/2

hence, tan[cos^-1(3/4) + sin^-1(3/4) - sec^-1(3) ] = tan[π/2 - sec^-1(3)]

Let sec^-1(3) = A

secA = 3 => tanA = √8 = 2√2 .........(1)

now, tan[π/2 - A] = cotA

= 1/tanA

= 1/2√2 [ from equation (1), ]

hence, option (d) is correct