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

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

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

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

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

Solution steps

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

Subtract

1 - sin^{2} (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = 0, cos (x) = 1

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 1 : x = 2 πn

Combine all the solutions

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

tan (\frac{2 x}{3}) = 0

3 cos^{2} (A) + 3 cos (A) = 0

3 csc (2 x) - 2 = 0

cos (3 x) (2 cos (x) + 1) = 0

3 csc (θ) - 1 = 0

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