Find the general solution of : 2(cos^2theta - sin^2 theta) = 1
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Answer:
Use the identity sin2x+cos2x=1.
2cos2θ−(1−cos2θ)=1
∴2cos2θ−1+cos2θ=1
∴3cos2θ=2
∴cos2θ=23
∴cosθ=±√23
∴θ=arccos√23+2πn,π−arccos√23+2πn,π+arccos√23+2πn,2π−arccos√23+2πn
∴θ=arccos√23+2πn,(2n+1)π−arccos√23,(2n+1)π+arccos√23,2π(1+n)−arccos√23
Hopefully this helps!
Step-by-step explanation:
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