# Question b88bf

Oct 4, 2017

See below

#### Explanation:

To Prove
$\cot \theta + \tan \theta = \sec \theta \csc \theta$

L.H.S.
$= \cot \theta + \tan \theta$

$\because \cot \theta = \cos \frac{\theta}{\sin} \theta \text{and} \tan \theta = \sin \frac{\theta}{\cos} \theta$

$= \cos \frac{\theta}{\sin} \theta + \sin \frac{\theta}{\cos} \theta$
Take LCM $S \int h \eta \cos \theta$
$= \frac{{\cos}^{2} \theta + {\sin}^{2} \theta}{\sin \theta \cos \theta}$
$= \frac{1}{\sin \theta \cos \theta}$

$\because \frac{1}{\sin} \theta = \csc \theta \text{and} \frac{1}{\cos} \theta = \sec \theta$

$= \sec \theta \csc \theta$

Oct 4, 2017

$\text{see explanation}$

#### Explanation:

$\text{using the "color(blue)"trigonometric identities}$

•color(white)(x)cottheta=costheta/sintheta" and "tantheta=sintheta/costheta"

•color(white)(x)cosectheta=1/sintheta" and "sectheta=1/costheta"

•color(white)(x)cos^2theta+sin^2theta=1

$\Rightarrow \cot \theta + \tan \theta$

$\implies \cos \frac{\theta}{\sin} \theta + \sin \frac{\theta}{\cos} \theta$

=>(cos^2theta+sin^2theta)/(sintheta×costheta)

=>1/(sinthetacostheta)=1/sintheta×1/costheta=csctheta×sectheta#