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Trigonometry: Solving Trigonometric Equations and Proving Identities

Manipulate trigonometric expressions, sketch graphs of trigonometric functions and solve equations.
Find the general solution of the following trigonometric equations:
1.a)cosθcos(pi/6)+sinθsin(pi/6) =0.25
b) 2sin^2 x - 5cosx+ 1 = 0
2. Prove: cos(θ+ pi/4) - sin(θ + pi/4) = 2cos(θ+ pi/4)


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Trigonometric equations are solved and identities are proven. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.