How do you solve 3sin^2(x) = cos^2(x)?

1 Answer
May 2, 2018

x = 30, 150, 210, 330

Explanation:

I'll be using theta to substitute as x and assuming the range of the value of theta is 0-360 degrees.

3sin^2theta = cos^2theta

By applying the formulae :

sin^2theta + cos^2theta = 1

=> sin^2theta = 1-cos^2theta

Thus,

3 (1 - cos^2theta) = cos^2theta

=> 3-3cos^2theta = cos^2theta

=> 3 = 4 cos^2theta

=> 3/4 = cos^2theta

=> +-sqrt(3/4) = cos theta

=> cos theta = sqrt (3/4) or cos theta = -sqrt(3/4)

:. theta : 30 , 150, 210, 330 in degrees.

You can check if the answer is correct by inserting the values calculated.

There you go, finished! :)