If 1 + sin2θ = 3sinθ cosθ, then prove that tanθ = 1 or1/2

Name: If 1 + sin2θ = 3sinθ cosθ, then prove that tanθ = 1 or 1 BY 2
Uploaded: Mon, 2021-02-01 15:07
Description: If 1 + sin2θ = 3sinθ cosθ, then prove that tanθ = 1 or 1 BY 2

If 1 + sin2θ = 3sinθ cosθ, then prove that tanθ = 1 or 1 BY 2

If 1 + sin²θ = 3sinθ cosθ, then prove that tanθ = 1 or1/2

Answers (1)

Solution. Given : 1 + sin²θ = 3sinθ cosθ
To Prove - tanθ = 1 or 1/2
Dividing both side by sinθ we get
$\frac{1+\sin ^{2}\theta }{\sin ^{2}\theta}= \frac{3\cos \theta }{\sin \theta }$
$\frac{1}{\sin ^{2}\theta}+\frac{\sin ^{2}\theta}{\sin ^{2}\theta}= 3\cot \theta$ $\left ( \because \frac{\cos \theta }{\sin \theta } = \cot \theta \right )$
$\cos ec^{2}\theta +1= 3\cot \theta$ $\left ( \because \frac{1}{\sin ^{2}\theta}= \cos ec^{2}\theta \right )$
$1+\cot ^{2}\theta +1= 3\cot \theta$ $\left ( \because \cos ec^{2}\theta = 1+\cot ^{2} \theta \right )$
$2+\cot ^{2} \theta+3\cot \theta= 0$
$\cot ^{2} \theta+3\cot \theta+2= 0$
$\cot ^{2} \theta-2\cot \theta-\cot \theta +2= 0$
$\cot \theta\left ( \cot \theta-2 \right )-1\left ( cot \theta-2\right )= 0$
$\left ( \cot \theta-2 \right )\left ( \cot \theta-1 \right )= 0$
$\cot \theta = 1,2$
We know that