Question

If 1 + sin^2 thetq = 3 sintheta costheta then prove that tan theta = 1

Answer 1

$tan\theta=1$

Step-by-step explanation:$1+sin^2\theta=3sin\theta cos\theta$

⇒$sin^2\theta+cos^2\theta+sin^2\theta=3sin\theta cos\theta$

⇒$2sin^2\theta+cos^2\theta=3sin\theta cos\theta$

We should divide it by $cos^2\theta$

⇒$\frac{2sin^2\theta}{cos^2\theta}+ \frac{cos^2\theta}{cos^2}=\frac{3sin\theta cos\theta}{cos^2\theta}</p><p>2tan^2\theta+1=3tan\theta$

Let$x=tan\theta$

⇒$2x^2+1=3x$

⇒$2x^2-3x+1=0$

By solving this quadratic equation,

⇒(2t-1)(t-1)=0

Either,t=1/2 or 1

⇒$tan\theta=1/2 or1$

⇒$tan\theta=1$

Hence Proved