What is the general solution for 2cos^2(x)-15cos(x)+7=0 ?

The general solution for 2cos^2(x)-15cos(x)+7=0 is x= pi/3+2pin,x=(5pi)/3+2pin

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2cos^2(x)-15cos(x)+7=0

2 cos^{2} (x) - 15 cos (x) + 7 = 0

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

2 cos^{2} (x) - 15 cos (x) + 7 = 0

Solve by substitution

cos (x) = 7, cos (x) = \frac{1}{2}

cos (x) = 7 :

No Solution

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

sec (θ) = - \frac{5}{4}

sin^{2} (x) - 4 sin (x) + 1 = 0

6 sin (2 x) + 2 sin (x) = 0

3 sin^{2} (w) - 4 sin (w) - 4 = 0

sin (θ) = \frac{9}{10}

What is the general solution for 2cos^2(x)-15cos(x)+7=0 ?
The general solution for 2cos^2(x)-15cos(x)+7=0 is x= pi/3+2pin,x=(5pi)/3+2pin