Question

The value of sin[2sin⁻¹(cosA)] is........,Select Proper option from the given options.
(a) sinA
(b) cosA
(c) cos2A
(d) sin2A

Answer 1

sin[2sin^(-1){sin(π/2-A)}],

sin[2(π/2-A)],

sin[π-2A],

sin2A

Answer 2

we have to find the value of sin[2sin^-1(cosA)]

Let 2sin^-1(cosA) = P Then, sin[sin^-1(cosA)] = sinP
now, 2sin^-1(cosA) = P
sin^-1(cosA) = P/2
sinP/2 = cosA ......(1)
so, cosP/2 = √(1 - cos²A) = sinA......(2)

we know, sin2x = 2sinx.cosx
so, sinP = 2sinP/2.cosP/2
= 2 × cosA.sinA [ from equations (1) and(2), ]
= 2sinA.cosA = sin2A

hence, sinP = sin2A
therefore option (d) is correct.