Question

latest determine the value of tan theta from the relation 5 sin square theta + 4 cos square theta equals to 9 by 2 ​

Answer 1

hope it helps you to know the solution

Answer 2

The value of tan theta is 1

Solution:

Given that,

$5\ sin^2\ \theta+4\ cos^2\ \theta = \frac{9}{2}$

We know that,

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

Therefore,

$5\ (1-cos^2\ \theta)+4\ cos^2\ \theta = \frac{9}{2}\\\\5 - 5cos^2\ \theta + 4\ cos^2\ \theta = \frac{9}{2}\\\\5-cos^2\ \theta = \frac{9}{2}\\\\cos^2\ \theta = 5 - \frac{9}{2}\\\\cos^2\ \theta = \frac{1}{2}\\\\Take\ square\ root\ on\ both\ sides\\\\cos\ \theta = \frac{1}{\sqrt{2}}$

$\theta = cos^{-1} \frac{1}{\sqrt{2}}\\\\\theta = 45$

Therefore,

$tan\ theta = tan\ 45 = 1$

Thus value of tan theta is 1

Learn more about this topic

If Sin 43 = m , find the value of Tan 47?

https://brainly.in/question/6245089

If tan theta + 1/tan theta = 2, find the value of tan square theta + 1/tan square theta

https://brainly.in/question/3881975