MathematicsIf y=cos-15cosx-12sinx13, x∈0,π2, then dydx is equal to

If $y = \cos^{- 1} (\frac{5 cosx - 12 sinx}{13}), x \in (0, \frac{π}{2}),$ then $\frac{dy}{dx}$ is equal to

Solution:

$\begin{array}{rcl} y & = & \cos^{- 1} (\frac{5}{13} \cos x - \frac{12}{13} \sin x) \\ = & \cos^{- 1} (\cos (x + α)) \\ = & x + α \end{array}$

Where $α = \tan^{- 1} (\frac{12}{5})$

Differentite

$\frac{d y}{d x} = 1$

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