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

The general solution for sin(x)=cos^2(x)-sin^2(x) is x= pi/6+2pin,x=(5pi)/6+2pin,x=(3pi)/2+2pin

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

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

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

Subtract

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

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

2 sin^{2} (x) = 2 + cos (x), 0 \leq x \leq 2 π

2 sin (θ) tan (θ) - tan (θ) = 0

sec (x) + 2 = 0

sin (x) + 1 = 0, 0 \leq x \leq 2 π

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

What is the general solution for sin(x)=cos^2(x)-sin^2(x) ?
The general solution for sin(x)=cos^2(x)-sin^2(x) is x= pi/6+2pin,x=(5pi)/6+2pin,x=(3pi)/2+2pin