Question

prove that :
$cot \alpha + tan \alpha = cosec \alpha \times sec \alpha$
​

Answer 1

$\huge\mathfrak\red{Given:-}$

$cot \alpha + tan \alpha = cosec \alpha \times sec \alpha$

$\huge\mathcal\blue{Solution:-}$

$\huge\mathcal\red{Iñ \: LHS:-}$

➡$cot \alpha + tan \alpha$

➡$cot \alpha = \frac{cos \alpha}{sin \alpha}$

➡$tan \alpha = \frac{sin \alpha}{cos \alpha}$

➡$\frac{cos^2 \alpha + sin^2 \alpha}{sin \alpha cos \alpha}$

➡$cos ^2\alpha + sin^2\alpha = 1$

➡$\frac{1}{cos \alpha ×sin \alpha}$

➡$\frac{1}{cos \alpha}×\frac{1}{sin \alpha}$

➡$\frac{1}{sin \alpha} = cosec \alpha$

and ;

➡$\frac{1}{cos \alpha} = sec \alpha$

So,

➡$cosec \alpha × sec \alpha$

$\mathcal\red{LHS \: is \: equal \: to \: RHS}$

Answer 2

Step-by-step explanation:

this is a correct answer