What is the general solution for (sin(x))/(cos(x))=1 ?

The general solution for (sin(x))/(cos(x))=1 is x= pi/4+pin

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(sin(x))/(cos(x))=1

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

x = \frac{π}{4} + πn

Degrees

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

Solution steps

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= tan (x)

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

9 (1 - cos (θ)) = sin^{2} (θ)

x, 1 = sin (x)

4 tan (x) sin (x) = - 5 sin (x)

9 cot^{2} (θ) - 4 = 0

4 sin^{2} (θ) = 1 + 4 cos (θ)

What is the general solution for (sin(x))/(cos(x))=1 ?
The general solution for (sin(x))/(cos(x))=1 is x= pi/4+pin