What is the general solution for cos(x)-sin(x)=0,\forall 0<= x<2pi ?

The general solution for cos(x)-sin(x)=0,\forall 0<= x<2pi is x= pi/4 ,x=(5pi)/4

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cos(x)-sin(x)=0,\forall 0<= x<2pi

cos (x) - sin (x) = 0, \forall 0 \leq x < 2 π

x = \frac{π}{4}, x = \frac{5 π}{4}

Solution steps

cos (x) - sin (x) = 0, \forall 0 \leq x < 2 π

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

Solutions for the range

0 \leq x < 2 π

x = \frac{π}{4}, x = \frac{5 π}{4}

3 sec (θ) + 2 = 8

sin^{2} (x) = 0.75

- 3 tan (θ) = 3

x, sin (x y) = cos (x + y)

2 sin (3 θ) - 1 = 0

What is the general solution for cos(x)-sin(x)=0,\forall 0<= x<2pi ?
The general solution for cos(x)-sin(x)=0,\forall 0<= x<2pi is x= pi/4 ,x=(5pi)/4