Question

$3tan\theta +cot\theta =5cosec\theta$. Solve for $\theta$, 0 ≤ $\theta$ ≤ 90.

__ (in degrees)

Answer 1

$\frac{3sin\theta }{cos\theta }+\frac{cos\theta }{sin\theta }=\frac{5}{sin\theta }$

$sin\theta (3si{n}^2\theta +co{s}^2\theta )=5sin\theta cos\theta$

$3(1-co{s}^2\theta )+co{s}^2\theta =5cos\theta$

$2co{s}^2\theta +5cos\theta -3=0$

$2cos\theta [cos\theta +3]-1(cos\theta +3)=0$

$(cos\theta +3)(2cos\theta -1)=0$

$cos\theta =-3orcos\theta =\frac{1}{2}$

$cos\theta$ = -3 is not possible as $cos\theta <1$

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

$\Rightarrow \theta ={60}^{\circ }$