Question

10sin^2 alpha+6cos^2 alpha=7
find the value of cot alpha​

Answer 1

$\large{\bf{\underline{\:\:\:\:\:\:Given\:that,\:\:\:\:\:\:\:\:}}}$

• $\bf{10\:sin^2\alpha+6\:cos^2\alpha=7}$

$\begin{gathered}\:\:\:\displaystyle{\sf{:\implies\:10\:sin^2\alpha+6(1-sin^2\alpha)=7}}\end{gathered}$

$\begin{gathered}\:\:\:{\sf{:\implies\:10\:sin^2\alpha+6-6\:sin^2\alpha=7}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:{\sf{:\implies\:4\:sin^2\alpha=7-6}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:{\sf{:\implies\sin^2\alpha=\frac{1}{4}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:\:{\sf{:\implies\sin\alpha=√\frac{1}{4}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:\:\:{\sf{:\implies\sin\alpha=±\frac{1}{2}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:\:\:\:\:{\sf{:\implies\sin\alpha=\frac{1}{2}[\frac{π}{2}<\alpha<π]}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:\:\:\:\:{\sf{:\implies\sin\alpha=sin(\frac{5π}{6})}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:\:\:\:\:\:{\sf{:\implies\alpha=\frac{5π}{6}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:\:\:\:\:{\sf{:\implies\cot\alpha=cot(\frac{5π}{6})}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:\:\:\:\:\:{\sf{:\implies\cot\alpha=\frac{1}{tan\frac{5π}{6}}}}\end{gathered}$

$\begin{gathered}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{\sf{:\implies\cot\alpha=-√3}}\end{gathered}$