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Q} Find dy/dx if y=sin^-1 x(3/5sinx + 4/5cosx )

Q} Find dy/dx
     if
 y=sin^-1 x(3/5sinx + 4/5cosx )

Grade:12

1 Answers

Nishant Vora IIT Patna
askIITians Faculty 2467 Points
9 years ago
Hello Student , Please find the solution.

y=sin^{-1} x(3/5sinx + 4/5cosx )
Let cosA=3/5 => so, sinA=4/5
So y=sin^{-1} x(cosA sinx +sinA cosx )
=> y=sin^{-1} x sin(A+x)
=> \frac{dy}{dx}=\frac{d(sin^{-1}x)}{dx} sin(A+x) + sin^{-1}x \frac{d(sin(A+x))}{dx}
=> \frac{dy}{dx}=\frac{1}{\sqrt{x^2 - 1}} sin(A+x) + sin^{-1}x * cos(A+x)
Now you can again expand sin(A+x) and Cos(A+x) and Put cosA=3/5 and sinA=4/5

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