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

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

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cos(θ)=sin(θ)

cos (θ) = sin (θ)

θ = \frac{π}{4} + πn

Degrees

θ = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

cos (θ) = sin (θ)

Rewrite using trig identities

cos (θ) = sin (θ)

Divide both sides by

cos (θ), cos (θ) \neq = 0

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

Simplify

1 = \frac{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

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

1 = tan (θ)

Switch sides

tan (θ) = 1

tan (θ) = 1

General solutions for

tan (θ) = 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}

θ = \frac{π}{4} + πn

θ = \frac{π}{4} + πn

3 tan^{2} (2 x) - 1 = 0

cos (θ) = - \frac{1}{4}

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

cos (x) = 3

sin (2 θ) = 3 cos (θ)

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