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CBSE Class 12-science Answered

x=2sinø–sin2ø , y=2cosø–cos2ø find d^2y÷dx^2
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Asked by rudrapandey14549 | 10 Jan, 2020, 06:32: PM
answered-by-expert Expert Answer
Given: x=2sinø–sin2ø , y=2cosø–cos2ø
To find d2y÷dx2
x equals 2 sin ϕ minus sin 2 ϕ
rightwards double arrow fraction numerator d x over denominator d ϕ end fraction equals 2 cos ϕ minus 2 cos 2 ϕ
rightwards double arrow fraction numerator d squared x over denominator d ϕ squared end fraction equals negative 2 sin ϕ plus 4 sin 2 ϕ
y equals 2 cos ϕ minus cos 2 ϕ
rightwards double arrow fraction numerator d y over denominator d ϕ end fraction equals negative 2 sin ϕ plus 2 sin 2 ϕ
rightwards double arrow fraction numerator d squared y over denominator d ϕ squared end fraction equals negative 2 cos ϕ plus 4 cos 2 ϕ
rightwards double arrow fraction numerator d squared y over denominator d x squared end fraction equals fraction numerator begin display style fraction numerator d squared y over denominator d ϕ squared end fraction end style over denominator begin display style fraction numerator d squared x over denominator d ϕ squared end fraction end style end fraction equals fraction numerator negative 2 cos ϕ plus 4 cos 2 ϕ over denominator negative 2 sin ϕ plus 4 sin 2 ϕ end fraction equals fraction numerator cos ϕ minus 2 cos 2 ϕ over denominator sin ϕ minus 2 sin 2 ϕ end fraction

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