Question

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

• A. 60°
• B. 45°
• C. 150°
• D. 30°

Answer 1

The correct option is A

60°

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

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

$3(1-co{s}^2\theta )+co{s}^2\theta =5cos\theta$
$2co{s}^2\theta +5cos\theta -3=0$
$2cos\theta [cos\theta +3]-1(cos\theta +3)=0$
($cos\theta +3\left)\right(2cos\theta -1)=0$

$cos\theta =-3$ (Not possible as $cos\theta$ ≤ 1)
$cos\theta =\frac{1}{2}$
$\Rightarrow \theta ={60}^{\circ }$