Question

Find solution of the equation $2si{n}^2\theta =3cos\theta$

Answer 1

The given equation can be expressed as 2$(1-co{s}^2\theta )=3cos\theta$

i.e. 2$co{s}^2\theta$ + 3 $cos\theta$ - 2 = 0

i.e. 2$co{s}^2\theta$ + 4$cos\theta$ - $cos\theta$ -2 = 0

i.e. 2$cos\theta$ ($cos\theta$ + 2) - 1($cos\theta$ + 2) = 0

i.e. (2$cos\theta$ - 1) ($cos\theta$ + 2) = 0

$\because$ $cos\theta$ = $\frac{1}{2}$ or $cos\theta$ = -2, which is in admissible an numerical value of $cos\theta$ cannot be greater than

1 or less than -1

$\because$ $cos\theta$ = $\frac{1}{2}$

i.e. $\theta$ = ${60}^{\circ }$