Question

Find the derivative of the following function:
f(x)= $\frac{sin(x+a)}{cosx}$

Answer 1

Here $f\left(x\right)=\frac{sin(x+a)}{cosx}$

$=\frac{cosx\frac{d}{dx}\left[sin\right(x+a\left)\right]-sin(x+a)\frac{d}{dx}\left(cosx\right)}{co{s}^{2}x}$

$=\frac{cosx.cos(x+a)-sin(x+a)(-sinx)}{co{s}^{2}x}$

$=\frac{cos(x+a-x)}{co{s}^{2}x}$

$[\because cos(A-B)=cosAcosB+sinAsinB]$

$=\frac{cosa}{co{s}^{2}x}$