Question

prove that tanA+ 1/tan A=secA×cosecA​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

1.

$1 + {tan}^{2} \theta \: = {sec}^{2} \theta \:$

TO PROVE

$\displaystyle \: tan\theta \: + \frac{1}{tan \theta \: } = sec \theta \: cosec \theta \:$

PROOF

$\displaystyle \: tan\theta \: + \frac{1}{tan \theta \: }$

$= \displaystyle \: \frac{ {tan}^{2} \theta + 1}{tan \theta}$

$= \displaystyle \: { {sec}^{2} \theta } \times {cot \theta}$

$= \displaystyle \: \frac{1}{ {cos}^{2} \theta \:} \times \frac{cos \theta}{sin \theta}$

$= \displaystyle \: \frac{1}{ {cos} \theta \:} \times \frac{1}{sin \theta}$

$\displaystyle \: = sec \theta \: cosec \theta \:$