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Question
If y =1 − cos θ, x = 1 − sin θ, then `dy/dx "at" θ =pi/4` is ______
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Solution
If y =1 − cos θ, x = 1 − sin θ, then `dy/dx "at" θ =pi/4` is −1
Explanation:
Given:
y = 1 − cosθ, x = 1 − sinθ
Differentiate w.r.t. θ
`dy/(d theta) = sin theta`
`dx/(d theta) = -cos theta`
`dy/dx = (dy/(d theta))/(dx/(d theta)) = sin theta/-cos theta = - tan theta`
`dy/dx = -tan (pi/4) =-1`
`dy/dx` at θ = π/4 = −1
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