Search:

(cosx)(tanx + sinxcotx) = sinx + cos^2 x

Taking left hand side and putting tanx = sinx/cosx and cotx = cosx/sinx

cosx(sinx/cosx + sinx*cosx/sinx)
= sinx + cos^2x

Hence proved

The probabilities of two persons A and B for telling the truth are 4/5 and 3/4 respectively. Find the probability that they contradict each other when asked about same topic ?