What is the general solution for -2sin(x/2)-1=-2cos(x/2)-1 ?

The general solution for -2sin(x/2)-1=-2cos(x/2)-1 is x= pi/2+2pin

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-2sin(x/2)-1=-2cos(x/2)-1

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

x = \frac{π}{2} + 2 πn

Solution steps

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

Subtract

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

from both sides

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

Rewrite using trig identities

2 - 2 tan (\frac{x}{2}) = 0

Move

2

to the right side

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

Divide both sides by

- 2

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

General solutions for

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

\frac{x}{2} = \frac{π}{4} + πn

Solve

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

x = \frac{π}{2} + 2 πn

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

tan (θ) = 30.48 (80)

cos (x) = a, \frac{3 π}{2} \leq x \leq 2 π

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

cos (x) = 0.77

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