Answer:
[tex]x=2r(1-cos \theta)[/tex]
Step-by-step explanation:
Given equation,
[tex]\frac{x}{2}=2r(\sin(\frac{\theta}{2}))^2[/tex]
[tex]\frac{x}{2}=2r\sin^2(\frac{\theta}{2})[/tex] ...... (1)
Since,
[tex]\cos 2A=1-2\sin^2 A[/tex]
[tex]\implies 2\sin^2A = 1 - \cos 2A[/tex]
Thus,
[tex]2 \sin^2(\frac{\theta}{2})=1-\cos \theta[/tex] ...... (2)
From equation (1) and (2),
[tex]\frac{x}{2}=r(1-\cos \theta)[/tex]
[tex]x=2r(1-\cos \theta)[/tex]
Which is the required formula.
