Find the general solution of the equation 5cos2θ + 7sin2θ – 6 = 0

Question

Find the general solution of the equation 5cos²θ + 7sin²θ – 6 = 0

Sum

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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Trigonometric Equations

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Q 27 Q 26 Q 28

Chapter 3: Trigonometric Functions - Exercise [Page 55]

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NCERT Exemplar Mathematics [English] Class 11

Chapter 3 Trigonometric Functions
Exercise | Q 27 | Page 55

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