Differentiate the following with respect of `x :(sin(x+a))/(cos x)`

Explanation

Given

`y=frac{sin (x+a)}{cos x}`

Differentiating both sides with respect to x

`frac{d y}{d x}=frac{cos x times frac{d}{d x} sin (x+a)-sin (x+a) times frac{d}{d x} cos x}{cos ^{2} x} `(Quotient rule )

`=frac{cos x times cos (x+a)-sin (x+a) times(-sin x)}{cos ^{2} x} `

`=frac{cos (x+a) cos x+sin (x+a) sin x}{cos ^{2} x} `

`=frac{cos (x+a-x)}{cos ^{2} x} `

`=frac{cos a}{cos ^{2} x}`