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Question
Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0
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Solution
5cos2θ + 7sin2θ – 6 = 0
We know that,
sin2θ = 1 – cos2θ
Therefore, 5cos2θ + 7(1 – cos2θ) – 6 = 0
⇒ 5cos2θ + 7 – 7cos2θ – 6 = 0
⇒ –2cos2θ + 1 = 0
⇒ cos2θ = `1/2`
Therefore, cosθ = `+- 1/sqrt(2)`
Therefore, cosθ = `cos pi/4` or cosθ = `cos (3pi)/4`
Since, the solution of cosx = cosα is given by,
x = 2mπ ± α ∀ m ∈ Z
θ = nπ ± `pi/4`, n ∈ Z
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