Question

Find all solutions in the interval [0, 2π). cos x = sin x

Answer 1

Cos x = Sin x

Sin x = Cos x
Sin x / Cos x = Cos x/ Cos x
Tan x = 1
tan(45) = 1

tan Θ = y/x ; 

x = π/4 ; 5π/4

Using the unit circle for cos x = sin x
sin Θ = y
cos Θ = x

x = y 
⇒ π/4 or 45° ⇒ (√2/2 , √2/2)
⇒ 5π/4 or 225° ⇒ (-√2/2 , -√2/2) 

Answer 2

Answer:

x= π/4,  5π/4

Step-by-step explanation:

Cos x = Sin x

find in  the unit circle for cos x = sin x

sin Θ = y

cos Θ = x

when x = π/4 ; x =y=√2/2

when x=5π/4 ;  x =y= -√2/2