Maharashtra State BoardHSC Arts 12th Board Exam
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Differentiate cos^-1((3cosx-2sinx)/sqrt13)  w. r. t. x. - Mathematics and Statistics

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Differentiate `cos^-1((3cosx-2sinx)/sqrt13)` w. r. t. x.

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Solution

`Let y=cos^-1((3cosx-2sinx)/sqrt13) `

`      =cos^-1(3/sqrt13cosx-2/sqrt13sinx)`

`Put cosA=3/sqrt13`

`sinA=sqrt(1-9/13)=2/sqrt13`

`y=cos^-1[cosAcosx-sinAsinx]`

`y=cos^-1[cos(A+x)]`

y = A + x, where A is a constant

`dy/dx=d/dx(A+x)=1`

Concept: Derivatives of Inverse Trigonometric Functions
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