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Grade 12Differential Calculus

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

milind

12 Years agoGrade 12

1 Answer

Jitender Singh

12 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

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