# C2 Trig question!

Find, in degrees, the value of Theta in the interval of 0<=Theta<360 for which:

2cos^2Theta cosTheta 1 = Sin^2Theta

Could somebody please work this out for me and show ALL their working, because I have NO idea how to do these sort of questions.
2cos²@ cos@ 1 = Sin²@

now sin²@ = 1- cos²@

2cos²@ cos@ 1 = 1 - cos²@
3 cos²@ - cos@ - 2 = 0
(3cos@ + 2) (cos@ - 1) = 0
cos@ = -2/3 or cos@ = 1
*girlie*
Find, in degrees, the value of Theta in the interval of 0<=Theta<360 for which:

2cos^2Theta cosTheta 1 = Sin^2Theta

Could somebody please work this out for me and show ALL their working, because I have NO idea how to do these sort of questions.

Well, first you have to use the trig identity sin^2theta + cos^2theta = 1
Which can be rearranged to give sin^2theta = 1 - cos^2theta
Substitution gives:
2 cos^2tgheta - costheta - 1 = 1 - cos^2theta
=> 3 cos^2theta - costheta -2 = 0
=> (3costheta + 2)(costheta - 1)=0
so, 3 costheta = -2, and costheta = 1
then solve for theta (Can't be bothered to do it)