What is the general solution for 5sin(θ/2)=5cos(θ/2) ?

The general solution for 5sin(θ/2)=5cos(θ/2) is θ= pi/2+2pin

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5sin(θ/2)=5cos(θ/2)

5 sin (\frac{θ}{2}) = 5 cos (\frac{θ}{2})

θ = \frac{π}{2} + 2 πn

Solution steps

5 sin (\frac{θ}{2}) = 5 cos (\frac{θ}{2})

Rewrite using trig identities

5 tan (\frac{θ}{2}) = 5

Divide both sides by

5

tan (\frac{θ}{2}) = 1

General solutions for

tan (\frac{θ}{2}) = 1

\frac{θ}{2} = \frac{π}{4} + πn

Solve

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

θ = \frac{π}{2} + 2 πn

tan (x) = \frac{80}{50}

- cos (x) + 4 cos (2 x) = 0

sin^{2} (x) + sin (x) - 2 = 0, 0 \leq x < 2 π

sin^{2} (x) + 5 sin (x) = 0

tan (α) = - \frac{4}{3}, \frac{π}{2} < α < π, cos (β) = \frac{1}{2}, 0 < β < \frac{π}{2}

What is the general solution for 5sin(θ/2)=5cos(θ/2) ?
The general solution for 5sin(θ/2)=5cos(θ/2) is θ= pi/2+2pin