# Find derivative of trigonometric function y=(3(1-sin x))/(2cos x)

Find derivative of trigonometric function $y=\frac{3\left(1-\mathrm{sin}x\right)}{2\mathrm{cos}x}$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

pivonie8
Simplify the trigonometric function
$y=\frac{3\left(1-\mathrm{sin}x\right)}{2\mathrm{cos}x}$
$y=\frac{3}{2}\left(\frac{1}{\mathrm{cos}x}-\left(\frac{\mathrm{sin}x}{\mathrm{cos}x}\right)\right)$
$y=\frac{3}{2}\left(\mathrm{sec}x-\mathrm{tan}x\right)\left\{\because \frac{1}{\mathrm{cos}x}=\mathrm{sec}x\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\frac{\mathrm{sin}x}{\mathrm{cos}x}=\mathrm{tan}x\right\}$
Derivative of trigonometric function:
$y=\frac{3}{2}\left(\mathrm{sec}x-\mathrm{tan}x\right)$
$\frac{dy}{dx}=\frac{d}{dx}\left(\frac{3}{2}\left(\mathrm{sec}x-\mathrm{tan}x\right)\right)$
$\frac{dy}{dx}=\frac{3}{2}\left(\frac{d}{dx}\left(\mathrm{sec}x\right)-\frac{d}{dx}\left(\mathrm{tan}x\right)\right)$
$\frac{dy}{dx}=\frac{3}{2}\left(\left(\mathrm{sec}x\cdot \mathrm{tan}x\right)-{\mathrm{sec}}^{2}x\right)\left\{\because \frac{x}{dx}\left(\mathrm{sec}x\right)=\left(\mathrm{sec}x\cdot \mathrm{tan}x\right)\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}d\left(dx\right)\left(\mathrm{tan}x\right)={\mathrm{sec}}^{2}x\right\}$
The derivative of function is given below
$\frac{dy}{dx}=\frac{3}{2}\left(\left(\mathrm{sec}x\cdot \mathrm{tan}x\right)-{\mathrm{sec}}^{2}x\right)$
Jeffrey Jordon