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Popular >

cos^2(x)= 1/2 (1+cos(x))

Solution

cos^{2} (x) = \frac{1}{2} (1 + cos (x))

Solution

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

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Solution steps

cos^{2} (x) = \frac{1}{2} (1 + cos (x))

Solve by substitution

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

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

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

Popular Examples

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

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

sin(3x)cos(x)+cos(3x)sin(x)=1

sin (3 x) cos (x) + cos (3 x) sin (x) = 1

2sin(x)cos(x)+2sin(x)-cos(x)-1=0

2 sin (x) cos (x) + 2 sin (x) - cos (x) - 1 = 0

sin(θ)tan^2(θ)-sin(θ)=0

sin (θ) tan^{2} (θ) - sin (θ) = 0

sin(x)= 4/5 ,sin(180-x)

sin (x) = \frac{4}{5}, sin (18 0^{\circ} - x)

Frequently Asked Questions (FAQ)

What is the general solution for cos^2(x)= 1/2 (1+cos(x)) ?
The general solution for cos^2(x)= 1/2 (1+cos(x)) is x=2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin