What is the general solution for 4cos^2(θ)=2,0<= θ<= 2pi ?

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

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4cos^2(θ)=2,0<= θ<= 2pi

4 cos^{2} (θ) = 2, 0 \leq θ \leq 2 π

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

Solution steps

4 cos^{2} (θ) = 2, 0 \leq θ \leq 2 π

Solve by substitution

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

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

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

Combine all the solutions

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

sin (θ) = \frac{21}{29}

3 tan (θ) + sec^{2} (θ) = 5

tan (t) = - \frac{3}{4}

sin (x) = - 0.47

sin (x) = - 0.85

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