Math, asked by pranay9212, 10 months ago

Please solve this problem friends !!

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Answers

Answered by Anonymous

108

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

$\\$

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

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

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

$\\$

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

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$\leadsto\:\:\:\sf\green {\dfrac {1+1+2\:cosA}{sinA+sinA\:cosA)}=4}$

$\\$

$\leadsto\:\:\:\sf\purple {\dfrac {2+2\:cosA}{sinA+sinA\:cosA}=4}$

$\\$

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

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$\leadsto\:\:\:\sf\purple {\dfrac {2}{sinA}=4}$

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$\leadsto\:\:\:\sf\green {2\:cosecA=2}$

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$\leadsto\:\:\: \sf\purple {cosecA=2}$

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$\leadsto\:\:\: \sf\underline\pink {cosec \:30^{\circ}=2}$

$\\$

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

Anonymous: Perfect :P

Answered by Anonymous

50

$\huge{\blue{\fbox{\purple{\bigstar{\mathbf{\red{hello\:mate}}}}}}}$

$\begin{lgathered}\\\end{lgathered}$

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

$\begin{lgathered}\\\end{lgathered}$

$[tex]\sf\underline\pink{Taking \ LCM}$

$\begin{lgathered}\\\end{lgathered}$

$\leadsto\:\:\sf {\dfrac {{sin}^{2}A+{(1+cosA)}^{2}}{sinA+sinA\:cosA}=4}$

$\begin{lgathered}\\\end{lgathered}$

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

$\begin{lgathered}\\\end{lgathered}$

$\leadsto\:\:\sf {\dfrac {1+1+2\:cosA}{sinA+sinA\:cosA)}=4}$

$\begin{lgathered}\\\end{lgathered}$

$\leadsto\:\:\sf {\dfrac {2+2\:cosA}{sinA+sinA\:cosA}=4}$

$\begin{lgathered}\\\end{lgathered}$

$\leadsto\:\:\:\sf {\dfrac {2 \cancel {(1+cosA)}}{sinA\cancel {(1+cosA)}}=4}$

$\leadsto\:\:\:\sf {\dfrac {2 \cancel {(1+cosA)}}{sinA\cancel {(1+cosA)}}=4}$

$\begin{lgathered}\\\end{lgathered}$

$\leadsto\:\:\:\sf {\dfrac {2}{sinA}=4}$

$\begin{lgathered}\\\end{lgathered}$

$\leadsto\:\:\:\sf {2\:cosecA=2}$

$\begin{lgathered}\\\end{lgathered}$

$\leadsto\:\:\: \sf {cosecA=2}$

$\begin{lgathered}\\\end{lgathered}$

$\leadsto\:\:\: \sf\underline {cosec \:30^{\circ}=2}$

$\begin{lgathered}\\\end{lgathered}$

$<body bgcolor="black"><marquee direction="left"><font color=red>$

$\huge {\bigstar {\mathfrak {\purple {Take\:care\:guyz...☺}}}}$

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