Question

If 7sinsquaretheta+3cossquaretheta=4 then the value of theta =?

Answer 1

$7 { \sin}^{2} \alpha + 3 { \cos}^{2} \alpha = 4$
$= > 3 \sin^{2} \alpha + 3 { \cos}^{2} \alpha = 4 - 4 { \sin}^{2} \alpha$
$= > 3( { \sin }^{2} \alpha + { \cos}^{2} \alpha ) = 4(1 - { \sin}^{2} \alpha )$
$= > 3 = 4 { \cos}^{2} \alpha$
$= > { \cos}^{2} \alpha = \frac{3}{4}$
$= > \cos \alpha = \frac{ \sqrt{3} }{2}$
$= > \cos( \alpha ) = \cos(30)$
$= > \alpha = 30$