Q.10. If sin 2   cos - 1 1 5 + cos 2   tan - 1 1 3 = p q , where p and q are relatively prime then digit at units place of p - q 2 k + 1 ,   k N , can be-
(A) 1
(B) 3
(C) 7
(D) 9

Use 2 sin-1x=sin-12x1-x22 tan-1x=cos-11-x21+x2sin 2 cos-115+cos 2 tan-113cos-1x=π2-sin-1x=sin 2π2-sin-115+cos cos-11-1321+132=sin π-2sin-115+cos cos-19-199+19=sin 2sin-115+cos cos-1810=sin sin-115×1-152+cos cos-1810=sin sin-115×5-15+cos cos-1810=sin sin-115×45+cos cos-1810=sin sin-115×25+cos cos-145=sin sin-125+cos cos-145=25+45=65Comparing with pqp=6, q=5p-q2k+1=6-52k+1=12k+1=1

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