Question

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

cos x = sin x

Answer 1

there are several ways to solve this problem

Answer 2

@mathsminds would factoring work for this problem?

Answer 3

\[\cos x = \sin x\]

Answer 4

divide both sides by cos x

Answer 5

\[\frac{ cosx }{ cosx }= \frac{ sinx }{ cosx }\]

Answer 6

\[tanx=1\]

Answer 7

\[x = \arctan(1)\]

Answer 8

\[x=\frac{ \pi }{ 4 }\]

Answer 9

@mathsmind and x = 5pi/4

Answer 10

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

Answer 11

if u know how to do that then all the best

Answer 12

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

Answer 13

ur solving for tan as being +ve

Answer 14

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

Answer 15

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

Answer 16

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