Question

1+sin theta/1-sin theta= (sec theta+tan theta) ²​

Answer 1

$LHS = \frac{(1+sin \theta )}{(1-sin \theta )}$

$= \frac{(1+sin \theta )(1+sin \theta)}{(1-sin \theta )(1+sin \theta)}$

$= \frac{(1+sin \theta )^{2}}{1^{2}-(sin \theta )^{2}}$

$= \frac{(1+sin \theta )^{2}}{cos \theta ^{2}}$

$= \Big( \frac{(1+sin \theta )}{cos \theta}\Big)^{2}$

$= \Big( \frac{1}{cos \theta }+ \frac{sin \theta }{cos \theta } \Big)^{2}$

$= ( sec \theta + tan \theta )^{2}$

$= RHS$

Therefore.,

$\red{ \frac{(1+sin \theta )}{(1-sin \theta )}}$

$\green {= ( sec \theta + tan \theta )^{2} }$

•••♪

Answer 2

Answer:

$\frac{(1+sin\alpha )}{1-sin\alpha } \\\\=\frac{sec\alpha+tan\alpha }{sec\alpha-tan\alpha} \\\\=\frac{(sec\alpha+tan\alpha )^{2} }{(sec\alpha)^2-(tan\alpha)^2} \\\\=\frac{(sec\alpha+tan\alpha )^{2} }{1}$                      

Step-by-step explanation: