When does 2cos(x)-2sin(x) equal zero?

Question

On the interval [0,2pi]?

 

 

Answer 1

The Function is 2cox(x) - 2sin(x).

Now Equate the function to zero.

2cox(x) - 2sin(x) = 0

cos(x) - sin(x) = 0

cos(x) = sin(x)

cos(x)/sin(x) = 1

cot(x) = 1

Then solutions of x are π/4 , 5π/4 , 9π/4  and so on.

Solutions between [0 , 2π] are π/4 and 5π/4.

Therefore the general Solution is π/4 and 5π/4.