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प्रश्न
Find `"dy"/"dx"` of the following function:
x = a(θ – sin θ), y = a(1 – cos θ)
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उत्तर
x = a(θ – sin θ) y = a(1 – cos θ)
`"dx"/("d"theta)` = a(1 - cosθ), `"dy"/("d"theta)` = a(0 - (- sin θ)) = a sin θ
`"dy"/"dx" = ("dy"/("d"theta))/("dx"/("d"theta))`
`= ("a" (2sin theta/2 cos theta/2))/(2 sin^2 theta/2)`
`= (cos theta/2)/(sin theta/2)`
`= cot theta/2`
∵ sin θ = 2 sin `theta/2` cos `theta/2`
1 - cos θ = 2 `sin^2 theta/2`
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