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How is sin^-1 x = cos^-1 Y is equals to. y = (1-x^2 )^ 1/2. Please explain sir

How is  sin^-1 x = cos^-1 Y  is equals to. y =  (1-x^2 )^ 1/2.    Please explain sir 

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
8 years ago
Ans:
sin^{-1}(x) = cos^{-1}(y)
Let
t = cos^{-1}(y)
cos(t) = coscos^{-1}(y)
cos(t) = y
sin(t) = \sqrt{1-y^{2}}
t = sin^{-1}(\sqrt{1-y^{2}})
sin^{-1}(x) = sin^{-1}(\sqrt{1-y^{2}})
\Rightarrow x = \sqrt{1-y^{2}}
Thanks & Regards
Jitender Singh
IIT Delhi
askIITian Faculty

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