Find the exact solutions to sin ( x ) = cos ( x ) in the interval [ 0 , 2 π ) in radians. If the equation has no solutions, respond with DNE.

Question

Please show the work thoroughly so I can understand.

Answer 1

If sinx = cosx, then dividing both sides by cosx gives tanx = 1

So, in the interval [0 , 2π], the solutions are π/4 and 5π/4.