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

The general solution for sin^2(2x)+cos(2x)=1 is x= pi/4+pin,x=(3pi)/4+pin,x=pin

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

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

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn, x = πn

Solution steps

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

Subtract

1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (2 x) = 0, cos (2 x) = 1

cos (2 x) = 0 : x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn

cos (2 x) = 1 : x = πn

Combine all the solutions

x = \frac{π}{4} + πn, x = \frac{3 π}{4} + πn, x = πn

sin (\frac{π}{x}) = 0

tan (x) = \frac{150}{80}

1 - 3 cos (x) = 1

cos (3 x) - cos (2 x) = 0

tan (2 x + 1 0^{\circ}) = 1.5

What is the general solution for sin^2(2x)+cos(2x)=1 ?
The general solution for sin^2(2x)+cos(2x)=1 is x= pi/4+pin,x=(3pi)/4+pin,x=pin