Prove that
sin ²0
cos²0
sino cos² sin
sin 0 cose
sin² y cos y sin
cos o
= sin (0-0) sin (p-w) sin (-0).
cos y
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Class 12
>>Maths
>>Continuity and Differentiability
>>Differentiation of Functions in Parametric Form
>>Find dy/dx , if x = 2costheta - cos 2th
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Find
dx
dy
, if x=2cosθ−cos2θ and y=2sinθ−sin2θ.
Medium
Solution
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Correct option is A)
Given, x=2cosθ−cos2θ and y=2sinθ−sin2θ
dθ
dx
=−2sinθ+2sin2θ
and
dθ
dy
=2cosθ−2cos2θ
∴
dx
dy
=
−2sinθ+2sin2θ
2cosθ−2cos2θ
=
sin2θ−sinθ
cosθ−cos2θ
=
2cos(
2
θ+2θ
)sin(
2
2θ−θ
)
2sin(
2
θ+2θ
)sin(
2
2θ−θ
)
=tan
2
3θ
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