What is the general solution for 2sin(x)=2cos(x) ?

The general solution for 2sin(x)=2cos(x) is x= pi/4+pin

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2sin(x)=2cos(x)

2 sin (x) = 2 cos (x)

x = \frac{π}{4} + πn

Degrees

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

Solution steps

2 sin (x) = 2 cos (x)

Rewrite using trig identities

2 sin (x) = 2 cos (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

2 tan (x) = 2

2 tan (x) = 2

Divide both sides by

2

2 tan (x) = 2

Divide both sides by

2

\frac{2 tan ( x )}{2} = \frac{2}{2}

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

3 csc^{2} (x) = 1 + 2 csc^{2} (x)

cos (2 x) + sin^{2} (x) = 1

3 (sec (θ)) = 10

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

4 sin^{3} (x) + 2 sin^{2} (x) = 2 sin (x) + 1

What is the general solution for 2sin(x)=2cos(x) ?
The general solution for 2sin(x)=2cos(x) is x= pi/4+pin