What is the general solution for cos(x-45)=(-1)/2 ?

The general solution for cos(x-45)=(-1)/2 is x=360n+165,x=360n+285

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cos(x-45)=(-1)/2

cos (x - 4 5^{\circ}) = \frac{- 1}{2}

x = 36 0^{\circ} n + 16 5^{\circ}, x = 36 0^{\circ} n + 28 5^{\circ}

Solution steps

cos (x - 4 5^{\circ}) = \frac{- 1}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

cos (x - 4 5^{\circ}) = - \frac{1}{2}

General solutions for

cos (x - 4 5^{\circ}) = - \frac{1}{2}

x - 4 5^{\circ} = 12 0^{\circ} + 36 0^{\circ} n, x - 4 5^{\circ} = 24 0^{\circ} + 36 0^{\circ} n

Solve

x - 4 5^{\circ} = 12 0^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 16 5^{\circ}

Solve

x - 4 5^{\circ} = 24 0^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} n + 28 5^{\circ}

x = 36 0^{\circ} n + 16 5^{\circ}, x = 36 0^{\circ} n + 28 5^{\circ}

x, sin (x + \frac{r}{4}) + sin (x - \frac{r}{3}) = 0

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

x, sec (x) - sin (50 o) = 2

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

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

What is the general solution for cos(x-45)=(-1)/2 ?
The general solution for cos(x-45)=(-1)/2 is x=360n+165,x=360n+285