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

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

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

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

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

Solution steps

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

Subtract

sin (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

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

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

Combine all the solutions

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

cos (24 0^{\circ})

arcsin (sin (\frac{7 π}{6}))

cos (arcsin (\frac{4}{5}))

2 sin (x) cos (x) = sin (x)

sin (2 x) = cos (2 x)

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