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Q   17 .     If     tan   y 2   =   a b ,   then   what   is   the   value   of   a   sin   y   +   cos   y   ? A )     0 B )   1 C )   a D )   b

tany2=ab                               ...(i)cosy2=ba2+b2           ...(ii)Now we have;asiny+bcosy=2asiny2cosy2+bcos2y2-sin2y2       {Since sin2θ=2sinθcosθ and cos2θ=cos2θ-sin2θ}=cos2y22asiny2cosy2cos2y2+bcos2y2-sin2y2cos2y2     {Multiplying and dividing by cos2y2}=cos2y22atany2+b1-tan2y2=ba2+b222a×ab+b1-a2b2                        {using (i) and (ii)}=b2a2+b22a2b+bb2-a2b2=b2a2+b22a2b+b2-a2b=b2a2+b2×a2+b2b=b
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