Question

Solve for A if,
$\frac{sin \: a}{1 + cos \: a} + \frac{1 + cos \: a \: }{sin \: a} = 4$
​

Answer 1

$\huge\bf\red{\underline{\underline{Solution}}}\::$

${\Large {\mathfrak {\orange{Given }}}}\begin{cases}\bf\blue{\dfrac {sin A}{1+cosA}+\dfrac {1+ cos A}{sin A} =4}\end{cases}$

$\rm\underline\pink{Taking \ LCM}$

$\longrightarrow\:\:\:\rm\purple {\dfrac {{sin}^{2}A+{(1+cosA)}^{2}}{sinA+sinA\:cosA}=4}$

$\boxed{\rm{\blue{{sin}^{2}\theta+{cos}^{2}\theta=1}}}$

$\longrightarrow\:\:\:\rm\green {\dfrac {1+1+2\:cosA}{sinA+sinA\:cosA)}=4}$

$\longrightarrow\:\:\:\rm\purple {\dfrac {2+2\:cosA}{sinA+sinA\:cosA}=4}$

$\longrightarrow\:\:\:\rm\green {\dfrac {2 \cancel {(1+cosA)}}{sinA\cancel {(1+cosA)}}=4}$

$\longrightarrow\:\:\:\rm\purple {\dfrac {2}{sinA}=4}$

$\longrightarrow\:\:\:\rm\green {2\:cosecA=2}$

$\longrightarrow\:\:\: \rm\purple {cosecA=2}$

$\longrightarrow\:\:\: \rm\underline\pink {cosec \:30^{\circ}=2}$

$\star\:\:{\underline{\underline{\orange{\boxed{\sf{A \ = \ 30^{\circ} }}}}}}$