What is the general solution for 4sin(x)=4cos(x) ?

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

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4sin(x)=4cos(x)

4 sin (x) = 4 cos (x)

x = \frac{π}{4} + πn

Degrees

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

Solution steps

4 sin (x) = 4 cos (x)

Rewrite using trig identities

4 sin (x) = 4 cos (x)

Divide both sides by

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

\frac{4 sin ( x )}{cos ( x )} = \frac{4 cos ( x )}{cos ( x )}

Simplify

\frac{4 sin ( x )}{cos ( x )} = 4

Use the basic trigonometric identity:

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

4 tan (x) = 4

4 tan (x) = 4

Divide both sides by

4

4 tan (x) = 4

Divide both sides by

4

\frac{4 tan ( x )}{4} = \frac{4}{4}

Simplify

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

sin (θ) + cos (θ) = - 1

6 sin (3 x) = 0

tan (x) = \frac{7}{24}

5 sin (x) = 2 cos^{2} (x) - 4

2 sin (x - \frac{π}{2}) + 2 = 0

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