Question

Find the derivative of:-
$\huge \boxed{ \green{ \sf {\: \frac{ \sin(x + a) }{ \cos(x) } }}}$
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Answer 1

Let

y =

$\frac{ \sin(x + a) }{ \cos(x) }$

We know that

Sin(X + a) = SinXcos(a) + CosX Sin(a)

on putting in above we get

$y = \tan(x) \cos( \alpha ) + \sin( \alpha )$

After differentiating we get

$\frac{dy}{dx} = { \sec(x) }^{2} \cos( \alpha )$

Answer 2

Answer:

Let

y =

\begin{lgathered}\frac{ \sin(x + a) }{ \cos(x) } \\\end{lgathered}cos(x)sin(x+a)

We know that

Sin(X + a) = SinXcos(a) + CosX Sin(a)

on putting in above we get

y = \tan(x) \cos( \alpha ) + \sin( \alpha )y=tan(x)cos(α)+sin(α)

After differentiating we get

\frac{dy}{dx} = { \sec(x) }^{2} \cos( \alpha )dxdy=sec(x)2cos(α)