Solve the equations 4cos2- - -3 - 2-3 - 1 cos-

(2cosθ 1)(2cosθ √(3))=0 ∴cosθ =1/2=cos (π /3) cosθ =√(3)/2=cos (π/6) ∴θ =2nπ±π/3 , θ =2nπ±π/6 . ...

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Standard XI

Mathematics

Solving Simultaneous Trigonometric Equations

Solve the equ...

Question

Solve the equations
$4 {cos}^{2} θ + \sqrt{3} = 2 (\sqrt{3} + 1) cos θ$ .

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Solution

$(2 cos θ - 1) (2 cos θ - \sqrt{3}) = 0$
$∴ cos θ = 1 / 2 = cos (π / 3)$
$cos θ = \sqrt{3} / 2 = cos (π / 6)$
$∴ θ = 2 n π \pm π / 3$ , $θ = 2 n π \pm π / 6$ .

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Solve the equations4cos2θ+√3=2(√3+1)cosθ.

(2cosθ−1)(2cosθ−√3)=0∴cosθ=1/2=cos(π/3)cosθ=√3/2=cos(π/6)∴θ=2nπ±π/3, θ=2nπ±π/6.

Solve the equations
$4 {cos}^{2} θ + \sqrt{3} = 2 (\sqrt{3} + 1) cos θ$ .

$(2 cos θ - 1) (2 cos θ - \sqrt{3}) = 0$
$∴ cos θ = 1 / 2 = cos (π / 3)$
$cos θ = \sqrt{3} / 2 = cos (π / 6)$
$∴ θ = 2 n π \pm π / 3$ , $θ = 2 n π \pm π / 6$ .