Question

$\sqrt\dfrac{ 1 + sin\ \theta}{1 - sin\ \theta}~is~equal~to$

• with full explanation​

Answer 1

Answer:

$\rm\sec θ + \tan θ$

Step-by-step explanation:

$\tt\sqrt\dfrac{ 1 + \sin \theta}{1 - \sin \theta}$

$\tt\sqrt{\dfrac{ 1 + \sin \theta}{1 - \sin \theta}×\dfrac{ 1 + \sin \theta}{1 +\sin \theta}}$

$\tt\sqrt{\dfrac{ (1 + \sin \theta)^2}{1 - \sin ^2 \theta}}$

$\tt \dfrac{ 1 + \sin \theta}{ \cos \theta}$

$\tt \dfrac{ 1 }{ \cos \theta}+\dfrac{ \sin \theta}{ \cos \theta}$

$\rm\sec θ + \tan θ$