What is the general solution for cos(x)+1-2sin^2(x)=0 ?

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

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

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

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

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

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

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

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

- 3 = tan (x)

sin (2 w) = 0

4 sin^{(2)} (θ) - 3 = 0

3 cos (5 t) = 0

cos^{2} (9 0^{\circ} - θ) = 1872

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