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

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

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

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

x = \frac{π}{4} + πn

Solution steps

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

Subtract

sin (x)

from both sides

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

Rewrite using trig identities

1 - tan (x) = 0

Move

1

to the right side

- tan (x) = - 1

Divide both sides by

- 1

tan (x) = 1

General solutions for

tan (x) = 1

x = \frac{π}{4} + πn

tan (x) + sec (x) = - 1

2 sin^{2} (θ) - cos (θ) - 1 = 0

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

8 sec^{2} (\frac{x}{2}) = 4

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

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