Question

Find value of $\theta$ :-
$2{\cos }^2\theta +11\sin \theta =7$

Answer 1

$2{\cos }^2\theta +11\sin \theta =7$

$2(1-{\sin }^2\theta )+11\sin \theta =7$

$2-2{\sin }^2\Theta +11\sin \theta =7$

$-2{\sin }^2\theta +11\sin \theta -5=0$

$-2{\sin }^2\theta -11\sin \theta +5=0$

$2{\sin }^2\theta -10\sin \theta -\sin \theta +5=0$

$2\sin \theta (\sin \theta -5)-1(\sin \theta -5)=0$

$(\sin \theta -5)(2\sin \theta -1)=0$

$\sin \theta \ne 5$, $\sin \theta =\frac{1}{2}$

$\theta =\frac{\pi }{6}$