Question

cos⁻¹(x/5)+cosec⁻¹(5/4)=π/2,then the value of x is.......,Select Proper option from the given options.
(a) 1
(b) 3
(c) 5
(d) 4

Answer 1

we have, cos^-1(x/5) + cosec^-1(5/4) = π/2

=> cos^-1(x/5) = π/2 - cosec^-1(5/4)

Let , cosec^-1(5/4) = A

cosecA = 5/4 => sinA = 4/5 .......(1)

now, cos^-1(x/5) = π/2 - A

=> x/5 = cos(π/2 - A)

=> x/5 = sinA

=> x = 5sinA

from equation (1), sinA = 4/5

x = 5 × 4/5 = 4

hence, option (d) is correct

Answer 2

In the attachment I have answered this problem.         Option (d) is correct.            See the attachment for detailed solution.