Question

if 5 sin theta -12 cos theta =0 then find the value of cosec theta and cot theta . here theta is an acute angle

Answer 1

$\textbf{ Given:}$

$5\;sin\theta-12\;cos\theta=0$

$\implies\frac{sin\theta}{cos\theta}=\frac{12}{5}$

$\impliest\;tan\theta =\frac{12}{5}$

$\text{Taking recirprocals,}$

$\cot\theta=\frac{5}{12}$

$\text{Using,}$

$\boxed{\bf\;cosec^2\theta-cot^2\theta=1}$

$\implies\;cosec^2\theta=1+cot^2\theta$

$=1+\frac{25}{144}$

$=\frac{144+25}{144}$

$=\frac{169}{144}$

$\implies\boxed{\bf\;cosec\theta=\frac{13}{12}}$