Question

2 cos^2 theta + sin theta -2 = 0
Where theta is a acute angle. Find the value of theta

Answer 1

$\huge \red{Question \: }$

$2cos^{2} \theta \: + sin \: \theta \: - 2 = 0 \: where \: \theta \: is \:acute \: \angle. \: Then \: find \theta \: \:$

$\huge \red{Answer}$

$= > 2cos^{2} \theta + sin \: \\theta \: - 2 = 0 \\ \\ = > 2(1 -sin^{2} \theta) + sin \: \theta - 2 = 0 \\ \\ = > 2 - 2sin ^{2} \theta + sin \: \theta - 2 = 0 \\ \\ = > 2sin ^{2} \theta - sin \: \theta \: = 0 \\ \\ = > sin \: \theta(2sin \: \theta - 1) = 0 \\ \\ \red{\bold {= > either}} \\ = > sin \: \theta = 0 \\ \\ = > \theta = 0 \\ \\ \red{\bold{= > or \: }} \\ sin \: \theta = \frac{1}{2} \\ \\ = > \theta = 30 \degree$