Solve the equation for - -4cos 3 - -3cos- -0-

4cos ^ 3 α #160; 3cosα #160; =0 ⇒cos 3α #160; =0 ⇒ 3α =(2n+1)π #160; 2 ...

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Relation between Roots and Coefficients for Quadratic

Solve the equ...

Question

Solve the equation for $α : 4 {cos}^{3} α - 3 cos α = 0$ .

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Solution

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32 t a n^{8} θ = 2 c o s^{2} α - 3 c o s α a n d 3 c o s^{3} θ + 6 c o s^{2} θ - 2 c o s θ - 4 = 0

α

{cos}^{3} (α + θ) {sin}^{3} (β - γ) + {cos}^{3} (β + θ) {sin}^{3} (γ - α) + {cos}^{3} (γ + θ) {sin}^{3} (α - β)

= 3 cos (α + θ) cos (β + θ) cos (γ + θ) \times sin (α - β) sin (β - γ) sin (γ - α)

α

cos α = cot α

32 t a n^{8} θ = 2 c o s^{2} α - 3 c o s α

3 c o s 2 θ = 1

α

α

{max}_{θ ϵ R} {5 s i n θ + 3 s i n (θ - α)} = 7

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