Find all solutions in the interval [0, 2π).

cos x = sin x

Question

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

anonymous · Answer

there are several ways to solve this problem

anonymous · Answer

@mathsminds would factoring work for this problem?

anonymous · Answer

$$\cos x = \sin x$$

anonymous · Answer

divide both sides by cos x

anonymous · Answer

$$\frac{ cosx }{ cosx }= \frac{ sinx }{ cosx }$$

anonymous · Answer

$$tanx=1$$

anonymous · Answer

$$x = \arctan(1)$$

anonymous · Answer

$$x=\frac{ \pi }{ 4 }$$

anonymous · Answer

@mathsmind and x = 5pi/4

anonymous · Answer

i want to show u how to get all the solutions between [0.2pi]

anonymous · Answer

if u know how to do that then all the best

anonymous · Answer

do u want to see another method of how to solve this question or not?

anonymous · Answer

ur solving for tan as being +ve

anonymous · Answer

@mathsmind no, thank you! those were the two solutions and I figured it out through your first method :)

anonymous · Answer

and u know that tan will be +ve in the first quarter and the third quarter is +ve

anonymous · Answer

but by the way u can't use that first method always, this is just a special case which u can do so, however u should get to the habit of using trig identities