What is the general solution for 2cos^2(x)-1=0,0<= x<2pi ?

The general solution for 2cos^2(x)-1=0,0<= x<2pi is x= pi/4 ,x=(7pi)/4 ,x=(3pi)/4 ,x=(5pi)/4

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2cos^2(x)-1=0,0<= x<2pi

2 cos^{2} (x) - 1 = 0, 0 \leq x < 2 π

x = \frac{π}{4}, x = \frac{7 π}{4}, x = \frac{3 π}{4}, x = \frac{5 π}{4}

Solution steps

2 cos^{2} (x) - 1 = 0, 0 \leq x < 2 π

Solve by substitution

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

cos (x) = \frac{1}{2}, 0 \leq x < 2 π : x = \frac{π}{4}, x = \frac{7 π}{4}

cos (x) = - \frac{1}{2}, 0 \leq x < 2 π : x = \frac{3 π}{4}, x = \frac{5 π}{4}

Combine all the solutions

x = \frac{π}{4}, x = \frac{7 π}{4}, x = \frac{3 π}{4}, x = \frac{5 π}{4}

cos (x + \frac{π}{2}) = sin (x)

cos (x) tan (x) + cos (x) = 0

2 sin^{2} (2 θ) = 1 + sin (2 θ)

sin (2 x) - cos (x) = 0, 0 \leq x \leq 2 π

csc (θ) = - \frac{2}{3}

What is the general solution for 2cos^2(x)-1=0,0<= x<2pi ?
The general solution for 2cos^2(x)-1=0,0<= x<2pi is x= pi/4 ,x=(7pi)/4 ,x=(3pi)/4 ,x=(5pi)/4