# If tan θ=125, find the value of 1+sin θ1−sin θ.

Question:

If $\tan \theta=\frac{12}{5}$, find the value of $\frac{1+\sin \theta}{1-\sin \theta}$.

Solution:

Given: $\tan \theta=\frac{12}{5}$

We have to find the value of the expression $\frac{1+\sin \theta}{1-\sin \theta}$.

$A C=\sqrt{A B^{2}+B C^{2}}$

$=\sqrt{12^{2}+5^{2}}$

$=13$

$\Rightarrow \sin \theta=\frac{12}{13}$

Therefore,

$\frac{1+\sin \theta}{1-\sin \theta}=\frac{1+\frac{12}{13}}{1-\frac{12}{13}}$

$=25$

Hence, the value of the given expression is 25.