Question

4sec^2 theta - 7tan^2 theta =3 then sin theta =?

Answer 1

Given............

$4 sec^2\theta - 7 tan^2\theta=3$

$\implies 4 sec^2 \theta - 4 tan^2\theta - 3 tan^2 \theta = 3$

$\implies 4 ( sec^2 \theta - tan^2 \theta ) - 3 \tan^2 \theta = 3$

__________________________________________________

We know that :

$\boxed{sec^2\theta -tan^2\theta=1}$

____________________________________________________

$\implies 4\times 1 - 3-3 tan^2\theta=0$

$\implies 3 tan^2 \theta = 1$

$\implies tan^2\theta =\frac{1}{3}$

$\implies tan \theta = \frac{1}{\sqrt{3}}$

___________________________________________________

Now see the attachments .

We find that :

$tan\theta = tan30^0$

$\theta = 30^0$

$sin\theta = sin 30^0$

$sin \theta = \frac{1}{2}$

The value of →→→→ $sin\theta = \boxed{\frac{1}{2}}$

Hope it helps you

_____________________________________________________________________

Answer 2

this answer must help u