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Question
Find `dy/dx, if y = 12 (1 – cos t), x = 10 (t – sin t), -pi/2< t< pi/2`
Solution
y = 12 (1 – cost ), x = 10 (t – sint)
On differentiating with respect to t,
`dy/dx = 12(0 + sin t) = 12 sin t, dx/dt = 10(1 - cos t)`
`therefore dy/dx = (dy//dt)/(dx//dt)`
`= (12 sin t)/(10 (1 - cos t))`
`= (6 sin t) / (5 (1 - cos t))`
`= 6/5 [(2 sin t // 2 cos t // 2)/(2 sin^2 t //2)]`
`= 6/5 cot t /2`
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