1. If x = u cos a - y sin a and y = u sina + v cos a, where a is a
constant, show that
( * * () (2) - (2)
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Step-by-step explanation:
We have, cosy=xcos(a+y)→(1)
Differentiate both sides w.r.t. x
−siny
dx
dy
=cos(a+y)−xsin(a+y)
dx
dy
⇒
dx
dy
=
xsin(a+y)−siny
cos(a+y)
=
cos(a+y)
cosy
sin(a+y)−siny
cos(a+y)
=
cosysin(a+y)−sinycos(a+y)
cos
2
(a+y)
=
sina
cos
2
(a+y)
Since sin(A−B)=sinAcosB−sinBcosA
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