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Grade 12Differential Calculus

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

Faiz

11 Years agoGrade 12

1 Answer

Nishant Vora

11 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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