Question

7 sin² thita + 3 cos² thita = 4 ,
find
tan thita
and thita ??​

Answer 1

Answer:

The answer is $\tan\theta=\frac{1}{\sqrt 3},\theta=30^\circ$

Step-by-step explanation:

Given  $7\sin^2\theta+3\cos^2\theta=4$

         $\Rightarrow 7\sin^2\theta+3(1-\sin^2\theta)=4, \because \sin^2\theta+\cos^2\theta=1$

        $\Rightarrow 7\sin^2\theta-3\sin^2\theta=4-3$

        $\Rightarrow 4\sin^2\theta=1\\\Rightarrow \sin^2\theta=\frac{1}{4}\\\Rightarrow \sin\theta=\frac{1}{2}\\\therefore \theta=30^\circ$

and

       $\tan\theta=\tan(30^\circ)=\frac{1}{\sqrt 3}$