What is the general solution for sin(x+pi/2)-cos(x+(3pi)/2)=0 ?

The general solution for sin(x+pi/2)-cos(x+(3pi)/2)=0 is x= pi/4+pin

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sin(x+pi/2)-cos(x+(3pi)/2)=0

sin (x + \frac{π}{2}) - cos (x + \frac{3 π}{2}) = 0

x = \frac{π}{4} + πn

Solution steps

sin (x + \frac{π}{2}) - cos (x + \frac{3 π}{2}) = 0

Rewrite using trig identities

1 - tan (x) = 0

Move

1

to the right side

- tan (x) = - 1

Divide both sides by

- 1

tan (x) = 1

General solutions for

tan (x) = 1

x = \frac{π}{4} + πn

tan (x) = \frac{\frac{3}{2}}{\frac{1}{2}}

tan (2 x) + sec (2 x) = 11

- 8 sin (x) + 8 cos (2 x) = 0

tan^{2} (x) + 2 sec (x) + 2 = 0

sin (θ) = 1 + cos (θ)

What is the general solution for sin(x+pi/2)-cos(x+(3pi)/2)=0 ?
The general solution for sin(x+pi/2)-cos(x+(3pi)/2)=0 is x= pi/4+pin