What is the general solution for 20sin(x)=20cos(x) ?

The general solution for 20sin(x)=20cos(x) is x= pi/4+pin

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20sin(x)=20cos(x)

20 sin (x) = 20 cos (x)

x = \frac{π}{4} + πn

Degrees

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

Solution steps

20 sin (x) = 20 cos (x)

Rewrite using trig identities

20 sin (x) = 20 cos (x)

Divide both sides by

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

\frac{20 sin ( x )}{cos ( x )} = \frac{20 cos ( x )}{cos ( x )}

Simplify

\frac{20 sin ( x )}{cos ( x )} = 20

Use the basic trigonometric identity:

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

20 tan (x) = 20

20 tan (x) = 20

Divide both sides by

20

20 tan (x) = 20

Divide both sides by

20

\frac{20 tan ( x )}{20} = \frac{20}{20}

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

\frac{- 5 cot ( x )}{2} + \frac{7}{3} = - \frac{1}{6}

8.59 tan^{2} (θ) - 24 tan (θ) + 15.29 = 0

(csc (x)) = - csc (x) cot (x)

cot (x) = - \frac{4}{3}

\frac{cos ^{2} ( x )}{sin ^{2} ( x )} = 1

What is the general solution for 20sin(x)=20cos(x) ?
The general solution for 20sin(x)=20cos(x) is x= pi/4+pin