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*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.

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)

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