What is the general solution for 4sin(x/2)=4cos(x/2) ?

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

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4sin(x/2)=4cos(x/2)

4 sin (\frac{x}{2}) = 4 cos (\frac{x}{2})

x = \frac{π}{2} + 2 πn

Solution steps

4 sin (\frac{x}{2}) = 4 cos (\frac{x}{2})

Rewrite using trig identities

4 tan (\frac{x}{2}) = 4

Divide both sides by

4

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

tan^{2} (θ) + 8 tan (θ) + 9 = 0

2 tan^{2} (x) - 1 = 3 tan (x)

8 csc^{2} (x) - 2 cot (x) = 9

cos (d) = \frac{9}{15}

coth^{2} (x) + csch^{2} (x) = 2

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