What is the general solution for cos(x)+sin(x-1)=0 ?

The general solution for cos(x)+sin(x-1)=0 is x=-pi/4+1/2-2pin,x= 1/2-(5pi)/4-2pin

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cos(x)+sin(x-1)=0

cos (x) + sin (x - 1) = 0

x = - \frac{π}{4} + \frac{1}{2} - 2 πn, x = \frac{1}{2} - \frac{5 π}{4} - 2 πn

Solution steps

cos (x) + sin (x - 1) = 0

Rewrite using trig identities

2 cos (\frac{2 + π}{4}) cos (\frac{2 + π - 4 x}{4}) = 0

Divide both sides by

2 cos (\frac{2 + π}{4})

cos (\frac{2 + π - 4 x}{4}) = 0

General solutions for

cos (\frac{2 + π - 4 x}{4}) = 0

\frac{2 + π - 4 x}{4} = \frac{π}{2} + 2 πn, \frac{2 + π - 4 x}{4} = \frac{3 π}{2} + 2 πn

Solve

\frac{2 + π - 4 x}{4} = \frac{π}{2} + 2 πn : x = - \frac{π}{4} + \frac{1}{2} - 2 πn

Solve

\frac{2 + π - 4 x}{4} = \frac{3 π}{2} + 2 πn : x = \frac{1}{2} - \frac{5 π}{4} - 2 πn

x = - \frac{π}{4} + \frac{1}{2} - 2 πn, x = \frac{1}{2} - \frac{5 π}{4} - 2 πn

sin^{22} (x) = \frac{1}{2}

cos^{5} (x) = cos (x)

tan (x) = (\frac{1.8}{3.6})

sec (x + 3 0^{\circ}) = 2

y, arccos (\frac{y}{2}) = 5 lo g_{10} (\frac{x}{5})

What is the general solution for cos(x)+sin(x-1)=0 ?
The general solution for cos(x)+sin(x-1)=0 is x=-pi/4+1/2-2pin,x= 1/2-(5pi)/4-2pin