How do you solve $cos θ = sin θ$ $cos theta= sin theta$ ?

Question

45591 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-23T15:12:40

The answer is $\pm \frac{π}{4}$ $+-pi/4$

$cos (θ) = sin (θ)$ $cos(theta)=sin(theta)$

$cos (θ) = cos (\pm \frac{π}{2} - θ)$ $cos(theta)=cos(+-pi/2-theta)$ by trigonometric equivalences

$θ = \pm \frac{π}{2} - θ + 2 k π$ $theta=+-pi/2-theta+2kpi$ with $k$ $k$ any integer

$2 θ = \pm \frac{π}{2} + 2 k π$ $2theta=+-pi/2+2kpi$

$θ = \pm \frac{π}{4} + k π$ $theta=+-pi/4+kpi$

How do you solve cos theta= sin thetacosθ=sinθcos theta= sin theta?