Question

$\sqrt{ \ {sec}^{2} } + \sqrt{ {cosec}^{2} } = \tan + \cot$
plz give step by step explanation​

Answer 1

Question:-

$\sqrt{{Sec}^{2}+{Cosec}^{2}}$ = tan + cot.

Please give step by step explaination.

Answer:-

Given,

$\sqrt{{Sec}^{2}+{Cosec}^{2}}$

Solution,

$\sqrt{{sec}^{2}+{cosec}^{2}}$

$\implies$ $\sqrt\dfrac{1}{{cosec}^{2}}+\dfrac{1}{{Sin}^{2}}$

$\implies$ $\sqrt\dfrac{{sin}^{2}+{cosec}^{2}}{{cosec}^{2}.{sin}^{2}}$

$\implies$ $\sqrt\dfrac{1}{{cosec}^{2}.{sin}^{2}}$

$\implies$ $\dfrac{1}{Cosec.Sin}$

$\implies$ $\dfrac{{cosec}^{2}+{sin}^{2}}{cosec.Sin}$

$\implies$ $\dfrac{Sin}{cosec}$ +$\dfrac{Cosec}{sin}$

$\implies$ Cot + tan

Hence proved.

-Happies!!