Question

7sin²theta + 3cos²theta=4. find the value of theta​

Answer 1

Step-by-step explanation:

theta=30°. since sintheta=1/2

Answer 2

Answer:

$\theta = 30\degree$

Step-by-step explanation:

Given,

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

To Find :-

Value of "theta".

Solution :-

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

We can write :-

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

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

$4sin^2\theta + 3(sin^2\theta + cos^2\theta) = 4$

We know that :-

$sin^2\theta + cos^2\theta = 1$

$4sin^2\theta + 3(1) = 4$

$4sin^2\theta + 3 = 4$

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

$4sin^2\theta = 1$

$sin^2\theta = \dfrac{1}{4}$

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

$sin\theta = sin30\degree$

cancelling sin on both sides :-

$\theta = 30\degree$

$\therefore \theta = 30\degree$