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Question
Find `dy/dx`, if y = 12 (1 – cos t), x = 10 (t – sin t), `-pi/2 < t < pi/2`.
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Solution
y = 12 (1 – cos t), x = 10 (t – sin t)
On differentiating with respect to t,
`dy/dt` = 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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