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solve for x: sin -1 (1-x) - 2sin -1 x = pi/2

solve for x:


sin-1(1-x) - 2sin-1x = pi/2

Grade:12

2 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Dear

sin-1(1-x) - 2sin-1x = pi/2

sin-1(1-x)  = pi/2 + 2sin-1x

let x = sinΘ

so

sin-1(1-x)  = pi/2 + 2sin-1sinΘ

1-x = sin(pi/2 + 2Θ)

1-x = cos2Θ

1-x = 1-2sin2Θ

 1-x = 1-2x2

 x=2x2

x(2x-1) =0

x=0 ,1/2

x=1/2 is not satisfying the given equation so

final solution is x=0

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Badiuddin

Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago

Dear student,
Please find the attached solution to your problem below. sin-1(1-x) - 2sin-1x = pi/2

sin-1(1-x) = pi/2 + 2sin-1x
let, x = sinΘ
so sin-1(1-x) = pi/2 + 2sin-1sinΘ
1-x = sin(pi/2 + 2Θ)
1-x = cos2Θ
1-x = 1-2sin2Θ
1-x = 1-2x2
x=2x2
x(2x-1) =0
x=0 ,1/2
x=1/2 is not satisfying the given equation so
final solution is x=0

Hope it helps.
Thanks and regards,
Kushagra

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