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Question

If tanA=xsinB1xcosB and tanB=ysinA1ycosA, then the value of sinAsinB for all permissible values of A,B is

A
xy
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B
x+yxy
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C
yx
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D
y+xyx
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Solution

The correct option is A xy
tanA=xsinB1xcosBsinAcosA=xsinB1xcosBsinAxcosBsinA=xsinBcosAsinA=x(cosAsinB+cosBsinA)sinA=xsin(A+B)(1)
tanB=ysinA1ycosAsinBcosB=ysinA1ycosAsinBycosAsinB=ycosBsinBsinB=y(cosAsinB+cosBsinB)sinB=ysin(A+B)(2)
Now,
sinAsinB=xsin(A+B)ysin(A+B)sinAsinB=xy

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