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

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

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sin(x)=cos(x)

sin (x) = cos (x)

x = \frac{π}{4} + πn

Degrees

x = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

sin (x) = cos (x)

Rewrite using trig identities

sin (x) = cos (x)

Divide both sides by

cos (x), cos (x) \neq = 0

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

Simplify

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

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

tan (x) = 1

tan (x) = 1

General solutions for

tan (x) = 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}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

arccsc (2)

tan (\frac{5 π}{3})

cos (\frac{19 π}{12})

cos (7 π)

cos (1 0^{\circ})

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