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

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

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sin(a)=cos(a)

sin (a) = cos (a)

a = \frac{π}{4} + πn

Degrees

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

Solution steps

sin (a) = cos (a)

Rewrite using trig identities

sin (a) = cos (a)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

tan (a) = 1

tan (a) = 1

General solutions for

tan (a) = 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}

a = \frac{π}{4} + πn

a = \frac{π}{4} + πn

tan (a) = 2.0503

4 sin (x) = 3 csc (x) - 4

5 sin (θ) - 3 = 0

arctan (1 + x^{2}) = 0

θ, tan (θ) = - 1

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