Question

If cos(2sin⁻¹x)=1/9, then the value of x=.........,Select Proper option from the given options.
(a) 3/2
(b) 2/3
(c) 1/2
(d) 1

Answer 1

we have to find the value of x where, cos(2sin^-1x)=1/9

Let 2sin^-1x = A .........(1)
sinA/2 = x
cosA = 1 - 2sin²A/2 [ from formula]
= 1 - 2x²
cosA = 1 - 2x² .....................(2)

now, cos(2sin^-1x) = 1/9

=> cosA = 1/9 [ from equation (1), ]

=> 1 - 2x² = 1/9 [ from equation (2), ]

=> 1 - 1/9 = 2x²

=> 8/9 = 2x²

=> x = ±2/3

hence, value of x = 2/3 or -2/3

therefore option (b) is correct