Q.

If a = x sec θ+ y tanθ , b = x tanθ +ysecθ then x2y2 =

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a

a2+b2

b

b2-a2

c

a2  b2

d

a2b2

answer is A.

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Detailed Solution

  a=x secθ+y tanθ  b=x tanθ+y secθ  a2-b2=x2 sec2θ+y2 tan2θ+2xysecθ tanθ-x2tan2θ-y2sec2θ-2xy secθ tanθ =x2-y2 sec2θ-x2-y2 tan2θ =x2-y2 sec2θ-tan2θ =x2-y2  x2-y2=a2-b2      

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