x=sin³t/√cos2t,y=cos³t/√cos2t find dy/dx
Answers
Answered by
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Step-by-step explanation:
If x=
cos2t
sin
3
t
,y=
cos2t
cos
3
t
, then find
dx
dy
.
Easy
Solution
verified
Verified by Toppr
x=
cos2t
sin
3
t
y=
cos2t
cos
3
t
dx
dy
=
dt
dx
dt
dy
=
cos2t
cos2t
3sin
2
tcost+sin
3
t
2
cos2t
2sint
cos2t
cos2t
3cos
2
t(−sint)+cos
3
t
2
cos2t
2sin2t
=
3sin
2
t(3costcos2t+2sin
2
tcost)
−3cos
2
tsint(cos2t)+sin2tcos
3
t
=
sin
2
t(3costcos2t+2sin
2
t)cost
cos
2
t(−3sintcos2t+2sintcos
2
t)
=
sin
2
tcost(3cos2t+2sin
2
t)
cos
2
tsint(−3cos2t+2cos
2
t)
=
sint(3−6sin
2
t+2sin
2
t)
cost(−6cos
2
t+3+2cos
2
t)
=
3sint−4sin
3
t
3cost−4cos
3
t
=−
sin3t
cos3t
=−cot3t.
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