Question

Evaluatesin(pi/3) - cos(2pi/3)

Answer 1

cos(2π/3)can be expressed as,

`\cos ((2\pi)/(3))=\cos (\pi-(\pi)/(3))`

Since cos(π-x)=-cosx, we can write

`\cos (2\pi)/(3)=\cos (\pi-(\pi)/(3)_{})=-\cos (\pi)/(3)`

We know,

`\begin{gathered} \sin ((\pi)/(3))=\frac{\sqrt[]{3}}{2} \\ \cos (\pi)/(3)=(1)/(2) \end{gathered}`

Therefore,

`\begin{gathered} \sin (\pi)/(3)-\cos (2\pi)/(3)=\sin (\pi)/(3)-(-\cos (\pi)/(3)) \\ =\sin (\pi)/(3)+\cos (\pi)/(3) \\ =\frac{\sqrt[]{3}}{2}+(1)/(2) \\ =\frac{\sqrt[]{3}+1}{2} \end{gathered}`