34. If x=cosec A
cos A and y cosec A-cos A then prove that
(s?,)*(3*-1-0
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x+y = cosec a + cos a + cosec a - cos a
x+y=2cosec a
x-y = cosec a + cos a - (cosec a - cos a )
x-y = cosec a + cos a - cosec a + cos a
x-y = 2cosa
(2/x+y)2 + (x-y/2)2 - 1 = 0
L.H.S = 4 / 4cosec2 + 4cos2/4 - 1
= 1/cosec2 + cos2 - 1
= sin2 a + cos2 a - 1 [ sin2 + cos2 = 1 ]
= 1 - 1
= 0
L.H.S = R.H.S
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