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If x = 2 cos t - cos 2t , y = 2 sin t -...

If ` x = 2 cos t - cos 2t , y = 2 sin t - sin 2t`, then the value of
` |(d^(2) y)/(dx^(2))|_(t= pi//2 ) `is

A

`3/2`

B

`-5/2`

C

`5/2`

D

`-3/2`

Text Solution

Verified by Experts

The correct Answer is:
D
`(dx)/(dt) = - 2sin t + 2 sin 2t `
` (dy)/(dx) = 2 cot t - 2 cos 2t `
`(dy)/(dx) = (2 cos t - 2 cos 2t)/(- 2 sin t + 2 sin 2t) = (cos t - cos 2t)/(sin 2t - sin t)`
` = (2 sin "" (3t)/(2) sin ""(t)/(2))/(2 cos "" (3t)/(2) sin ""(t)/(2))= tan""(3t)/(2)`
`(d^(2)y)/(dx^(2) )= (d)/(dt) (tan "" (3t)/(2)) (dt)/(dx)`
` = (sec^(2) ""(3t)/(2))xx (3)/(2) (dt)/(dx)`
` (3)/(2) sec^(2) ""(3t)/(2) xx (1)/(-(2sin 2t - 2 sin t))`
`|(d^(2) y)/(dx^(2))|_(t = pi//2) = -(3)/(2)` .
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -MHT CET CORER
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