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

The general solution for sin(x-20)=cos(x) is x=-360n+55,x=-125-360n

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sin(x-20)=cos(x)

sin (x - 2 0^{\circ}) = cos (x)

x = - 36 0^{\circ} n + 5 5^{\circ}, x = - 12 5^{\circ} - 36 0^{\circ} n

Solution steps

sin (x - 2 0^{\circ}) = cos (x)

Subtract

cos (x)

from both sides

sin (x - 2 0^{\circ}) - cos (x) = 0

Rewrite using trig identities

- 2 sin (5 5^{\circ}) sin (\frac{198 0 ^{\circ} - 36 x}{36}) = 0

Divide both sides by

- 2 sin (5 5^{\circ})

sin (\frac{198 0 ^{\circ} - 36 x}{36}) = 0

General solutions for

sin (\frac{198 0 ^{\circ} - 36 x}{36}) = 0

\frac{198 0 ^{\circ} - 36 x}{36} = 0 + 36 0^{\circ} n, \frac{198 0 ^{\circ} - 36 x}{36} = 18 0^{\circ} + 36 0^{\circ} n

Solve

\frac{198 0 ^{\circ} - 36 x}{36} = 0 + 36 0^{\circ} n : x = - 36 0^{\circ} n + 5 5^{\circ}

Solve

\frac{198 0 ^{\circ} - 36 x}{36} = 18 0^{\circ} + 36 0^{\circ} n : x = - 12 5^{\circ} - 36 0^{\circ} n

x = - 36 0^{\circ} n + 5 5^{\circ}, x = - 12 5^{\circ} - 36 0^{\circ} n

x, z = sin^{2} (x - 2 π y)

sin (θ) = \frac{3}{3 5}

6 cos (θ) sin (θ) + cos (θ) = 0

cos (x) + cos (5 x) = 0

7 cos (t) + 5 sin (t) = 0

What is the general solution for sin(x-20)=cos(x) ?
The general solution for sin(x-20)=cos(x) is x=-360n+55,x=-125-360n