What is the general solution for sin(x+(3pi)/2)-cos(x+pi/2)=1 ?

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

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sin(x+(3pi)/2)-cos(x+pi/2)=1

sin (x + \frac{3 π}{2}) - cos (x + \frac{π}{2}) = 1

x = \frac{π}{2} + 2 πn, x = 2 πn + π

Solution steps

sin (x + \frac{3 π}{2}) - cos (x + \frac{π}{2}) = 1

Rewrite using trig identities

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

Subtract

1

from both sides

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

Rewrite using trig identities

- 1 + 2 sin (x - \frac{π}{4}) = 0

Move

1

to the right side

2 sin (x - \frac{π}{4}) = 1

Divide both sides by

2

sin (x - \frac{π}{4}) = \frac{2}{2}

General solutions for

sin (x - \frac{π}{4}) = \frac{2}{2}

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

Solve

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

Solve

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

x = \frac{π}{2} + 2 πn, x = 2 πn + π

csc (x) - cot (x) = 1

sin (x) = - \frac{1}{2} sin (2 x)

cot (2 x) = 1.732

sin (9 0^{\circ} - a) = \frac{1}{1.63}

cot^{2} (x) - cos^{2} (x) = - 1

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