How do you solve an equation with 2 trigonometric functions?

Let us take an example of an equation with two trigonometry functions, such as:

cos2(α) + cos(α) = sin2(α)

cos2(θ) + cos(θ) = 1-cos2(θ) [By trigonometry identities: Sin2(θ)+cos2(θ)=1]

2cos2(θ)+cos(θ)-1 = 0

[2cos(θ)-1][cos(θ)+1]=0

cos(θ) = ½ and cos(θ) = -1

Therefore,

θ = 60° or 180°

Check the list of trigonometry identities here at BYJU’S.

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