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Q.

1sin6x+cos6xdx is equal to

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a

tan1(tanx+cotx)+C

b

tan1(tanxcotx)+C

c

none of these

d

tan1(cotxtanx)+C

answer is C.

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Detailed Solution

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Let

    I=1sin6x+cos6xdx=sec6x1+tan6xdx I=1+tan2x21+tan6xsec2xdx

                 =1+t221+t6dt, where t=tanx

      I=t2+1t41t2+1dt=1+1t2t2+1t21dt=dt1tt1t2+12 I=tan1t1t+C=tan1(tanxcotx)+C

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