What is the general solution for tan(θ/2+pi/4)=1 ?

The general solution for tan(θ/2+pi/4)=1 is θ=2pin

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tan(θ/2+pi/4)=1

tan (\frac{θ}{2} + \frac{π}{4}) = 1

θ = 2 πn

Degrees

θ = 0^{\circ} + 36 0^{\circ} n

Solution steps

tan (\frac{θ}{2} + \frac{π}{4}) = 1

General solutions for

tan (\frac{θ}{2} + \frac{π}{4}) = 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

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

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

Solve

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

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

Subtract

\frac{π}{4}

from both sides

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

Simplify

\frac{θ}{2} = πn

Multiply both sides by

2

\frac{θ}{2} = πn

Multiply both sides by

2

\frac{2 θ}{2} = 2 πn

Simplify

θ = 2 πn

θ = 2 πn

θ = 2 πn

cos^{2} (x) - 4 cos (x) + 3 = 0

sin^{2} (x) + 2 sin (x) + 1 = 0

4 cos^{2} (x) = 2

sin (x) = - \frac{1}{5}

cos (2 x) + sin (2 x) = 0

What is the general solution for tan(θ/2+pi/4)=1 ?
The general solution for tan(θ/2+pi/4)=1 is θ=2pin