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

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

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cos(z)=sin(z)

cos (z) = sin (z)

z = \frac{π}{4} + πn

Degrees

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

Solution steps

cos (z) = sin (z)

Rewrite using trig identities

cos (z) = sin (z)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

1 = tan (z)

Switch sides

tan (z) = 1

tan (z) = 1

General solutions for

tan (z) = 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}

z = \frac{π}{4} + πn

z = \frac{π}{4} + πn

sin (x + 3) = sin (x)

4 sin^{2} (x) = \frac{csc ^{2} ( x )}{4}

2 sin (3 x) = 2

sin (x) = \frac{2}{3}

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

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