Question
Asked Nov 24, 2019
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find x

sin-1(1-x)-2sin-1x=90 degree

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Expert Answer

Step 1

sin-1(1-x)-2sin-1x=90 degree

2 sin x-
2
sin1 (1
-2 sin -sin"(1-x)
-2 sin1 cos(1-x)
...i)
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2 sin x- 2 sin1 (1 -2 sin -sin"(1-x) -2 sin1 cos(1-x) ...i)

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Step 2

Let sin-1(x) = a hence our equation becomes,

-2a cos (1-x
cos (-2a) 1-x
cos (2a) 1x
cos(-x)cos (x)
(cos 2a 1-2sin2a)
1-2sin a 1-x
now sinx a
-2[sin(sin"x)] 1-x
1-2x2 1-x
2x2x0
x(2x 1)0
1
x = 0
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-2a cos (1-x cos (-2a) 1-x cos (2a) 1x cos(-x)cos (x) (cos 2a 1-2sin2a) 1-2sin a 1-x now sinx a -2[sin(sin"x)] 1-x 1-2x2 1-x 2x2x0 x(2x 1)0 1 x = 0

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Step 3

Bur x = ½ does not satisfy th...

sin (1 2sin x=
1
2 sin
1
sin
- 2 sin
2
2
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sin (1 2sin x= 1 2 sin 1 sin - 2 sin 2 2

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Math

Trigonometry

Trigonometric Ratios