What is the general solution for cos(p)-sin(p)=1 ?

The general solution for cos(p)-sin(p)=1 is p=(3pi)/2+2pin,p=2pi+2pin

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cos(p)-sin(p)=1

cos (p) - sin (p) = 1

p = \frac{3 π}{2} + 2 πn, p = 2 π + 2 πn

Solution steps

cos (p) - sin (p) = 1

Subtract

1

from both sides

cos (p) - sin (p) - 1 = 0

Rewrite using trig identities

- 1 - 2 sin (\frac{4 p - π}{4}) = 0

Move

1

to the right side

- 2 sin (\frac{4 p - π}{4}) = 1

Divide both sides by

- 2

sin (\frac{4 p - π}{4}) = - \frac{2}{2}

General solutions for

sin (\frac{4 p - π}{4}) = - \frac{2}{2}

\frac{4 p - π}{4} = \frac{5 π}{4} + 2 πn, \frac{4 p - π}{4} = \frac{7 π}{4} + 2 πn

Solve

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

Solve

\frac{4 p - π}{4} = \frac{7 π}{4} + 2 πn : p = 2 π + 2 πn

p = \frac{3 π}{2} + 2 πn, p = 2 π + 2 πn

x, y = 2 sin (x)

2 cos (3 x) + cos (2 x) + 1 = 0

4 + 2 tan^{2} (θ) = 5 tan^{2} (θ) + 3

sin (x) = sin (\frac{π}{5})

x, sin (2 x) = cos (2 x)

What is the general solution for cos(p)-sin(p)=1 ?
The general solution for cos(p)-sin(p)=1 is p=(3pi)/2+2pin,p=2pi+2pin