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

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

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

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

x = \frac{3 π}{2} + 2 πn

Solution steps

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

Rewrite using trig identities

tan (\frac{x}{2}) = - 1

General solutions for

tan (\frac{x}{2}) = - 1

\frac{x}{2} = \frac{3 π}{4} + πn

Solve

\frac{x}{2} = \frac{3 π}{4} + πn : x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

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

5 cos (x) cot (x) - 3 cos (x) - 10 cot (x) + 6 = 0

cos (x) = \frac{- 1}{2}

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

y, cos (y) = x

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