Question

If sin⁻¹(1-x)-2sin⁻¹x=π/2, then x is.......,Select Proper option from the given options.
(a) - 1/2
(b) 0
(c) 1/3
(d) 1/2

Answer 1

HELLO DEAR,



let  sin-¹(1 - x) = A  ,   So  Sin A  = 1-x
let  Sin-¹x = B,     So Sin B = x 


NOW,
GIVEN:-
A - 2 * B = π/2
 
A  - π/2  = 2B

taking cosine both side,

Cos(A - π/2)  = Cos (2B)
 
[cos(-b) = cosb]

cos(π/2 - A) =  1 - 2 Sin² B 

sinA = 1 - 2sin²B
 
1 - x   = 1 - 2 x² 
 
2 x² - x = 0

x(2x - 1) = 0
 
x = 0 or , x = 1/2


I HOPE ITS HELP YOU DEAR,
THANKS