What is the general solution for sin^2(θ)=cos(θ)+cos^2(θ) ?

The general solution for sin^2(θ)=cos(θ)+cos^2(θ) is θ=pi+2pin,θ= pi/3+2pin,θ=(5pi)/3+2pin

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sin^2(θ)=cos(θ)+cos^2(θ)

sin^{2} (θ) = cos (θ) + cos^{2} (θ)

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

Solution steps

sin^{2} (θ) = cos (θ) + cos^{2} (θ)

Subtract

cos (θ) + cos^{2} (θ)

from both sides

sin^{2} (θ) - cos (θ) - cos^{2} (θ) = 0

Rewrite using trig identities

1 - cos (θ) - 2 cos^{2} (θ) = 0

Solve by substitution

cos (θ) = - 1, cos (θ) = \frac{1}{2}

cos (θ) = - 1 : θ = π + 2 πn

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

Combine all the solutions

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

7 cos (θ) = 2 + 9 cos (θ)

sec (x) \cdot cot (x) - 2 cot (x) + sec (x) = 2

3 sin^{2} (x) - 10 sin (x) - 8 = 0

2 \cdot 9.8 \cdot L (1 - cos (θ)) = 0.018

cos (7 x) = sin (4 x + 2)

What is the general solution for sin^2(θ)=cos(θ)+cos^2(θ) ?
The general solution for sin^2(θ)=cos(θ)+cos^2(θ) is θ=pi+2pin,θ= pi/3+2pin,θ=(5pi)/3+2pin