What is the general solution for cos(2x)-7cos(x)-3=0 ?

The general solution for cos(2x)-7cos(x)-3=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin

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cos(2x)-7cos(x)-3=0

cos (2 x) - 7 cos (x) - 3 = 0

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Solution steps

cos (2 x) - 7 cos (x) - 3 = 0

Rewrite using trig identities

- 4 + 2 cos^{2} (x) - 7 cos (x) = 0

Solve by substitution

cos (x) = 4, cos (x) = - \frac{1}{2}

cos (x) = 4 :

No Solution

cos (x) = - \frac{1}{2} : x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Combine all the solutions

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

tan^{2} (4 5^{\circ} - \frac{x}{3}) = 0.58

- 20 csc (x) = 40

0 = 4 ∣ sin (6 θ) ∣

5 sin^{2} (θ) - 11 sin (θ) + 6 = 0

cos (x) = \frac{11}{14}, sin (x)

What is the general solution for cos(2x)-7cos(x)-3=0 ?
The general solution for cos(2x)-7cos(x)-3=0 is x=(2pi)/3+2pin,x=(4pi)/3+2pin