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Popular >

1-2cos^2(x)-cos(x)=0

Solution

1 - 2 cos^{2} (x) - cos (x) = 0

Solution

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

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Solution steps

1 - 2 cos^{2} (x) - cos (x) = 0

Solve by substitution

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

cos (x) = - 1 : x = π + 2 πn

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

Combine all the solutions

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

Popular Examples

1/3 =cos((pix)/(12))

\frac{1}{3} = cos (\frac{π x}{12})

(cos(30))/(cos(60))=tan(x)

\frac{cos ( 3 0 ^{\circ} )}{cos ( 6 0 ^{\circ} )} = tan (x)

4cos^2(x)-18cos(x)-10=0

4 cos^{2} (x) - 18 cos (x) - 10 = 0

25sin(θ)-1.5cos(θ)=20

25 sin (θ) - 1.5 cos (θ) = 20

sin((2θ)/3)= 1/2 ,0<= θ<= 2pi

sin (\frac{2 θ}{3}) = \frac{1}{2}, 0 \leq θ \leq 2 π

Frequently Asked Questions (FAQ)

What is the general solution for 1-2cos^2(x)-cos(x)=0 ?
The general solution for 1-2cos^2(x)-cos(x)=0 is x=pi+2pin,x= pi/3+2pin,x=(5pi)/3+2pin