Question
If 7sin² ϕ + 3cos² ϕ = 4, then find the
value of ϕ ?Solution
7sin² ϕ + 3cos² ϕ = 4sin² ϕ + 3sin² ϕ +3cos² ϕ = 4 4sin² ϕ + 3(sin2 ϕ + cos2 ϕ) = 4 4sin²ϕ + 3 (1) = 4 4sin²ϕ + 4 - 3 = 1 4sin²ϕ = 1 sin²ϕ = 1/4 sin ϕ = 1/2 sin30° = 1/2 Hence, ϕ = 30
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