What is the general solution for tan(pi+c)=1 ?

The general solution for tan(pi+c)=1 is c= pi/4+pin-pi

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tan(pi+c)=1

tan (π + c) = 1

c = \frac{π}{4} + πn - π

Degrees

c = - 13 5^{\circ} + 18 0^{\circ} n

Solution steps

tan (π + c) = 1

General solutions for

tan (π + c) = 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}

π + c = \frac{π}{4} + πn

π + c = \frac{π}{4} + πn

Solve

π + c = \frac{π}{4} + πn : c = \frac{π}{4} + πn - π

π + c = \frac{π}{4} + πn

Move

π

to the right side

π + c = \frac{π}{4} + πn

Subtract

π

from both sides

π + c - π = \frac{π}{4} + πn - π

Simplify

c = \frac{π}{4} + πn - π

c = \frac{π}{4} + πn - π

c = \frac{π}{4} + πn - π

8 sin^{2} (x) = 8 cos^{2} (x)

sin (x) = \frac{6}{8}

tan (x) = 2 + tan (3 x)

2 sin (x) - 3 = 0

sin^{2} (x) = 2 sin^{2} (\frac{x}{2})

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