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प्रश्न
Find y2 for the following function:
x = a cosθ, y = a sinθ
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उत्तर
x = a cos θ, y = a sin θ
`"dx"/("d"θ)`= a(-sinθ) = -a sinθ …….. (i)
`"dy"/("d"θ)` = a(cosθ)
`therefore y_1 = "dy"/"dx" = ("dy"/("d"θ))/("dx"/("d"θ)) = ("a" cos theta)/(- "a" sin theta)`
`y_1 = "dy"/"dx"` = - cot θ
`y_2 = ("d"^2y)/"dx"^2 = - (- "cosec"^2 theta) ("d"theta)/"dx"`
`= "cosec"^2theta ("d"theta)/"dx"`
`= "cosec"^2theta 1/("dx"/("d"theta))`
`=> "cosec"^2 theta xx ("cosec" theta)/(- "a")`
`= (- 1)/"a" "cosec"^3 theta`
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