Question

if 5 sin square theta + 3 cos square =4 then find the value of sin theta and cos theta

Answer 1

Answer:

Here is the answer.

Step-by-step explanation:

Given,

$5 {sin}^{2}\theta + 3 {cos}^{2} \theta = 4 \\ = > 5 {sin}^{2} \theta + 3(1 - {sin}^{2} \theta) = 4 \\ = > 5 {sin}^{2} \theta + 3 - 3 {sin}^{2} \theta = 4 \\ = > 2 {sin}^{2} \theta = 4 - 3 \\ = > {sin}^{2} \theta = \frac{1}{2} \\ = > sin\theta = \sqrt{ \frac{1}{2} } \\ = > sin\theta = \frac{1}{ \sqrt{2} }$

$\therefore \: sin\theta = \frac{1}{ \sqrt{2} } \\ = > sin\theta = sin45\degree \\ = > \theta = 45\degree$

$\therefore \: cos\theta \\ = cos45\degree \\ = \frac{1}{ \sqrt{2} }$