Question

in a triangle ABC right angled at C if tan a is equal to 1 by root 3 and 10 B root 3 so that sin a cos b + Cos A

Answer 1

In the given right angled triangle

tan A = 1/root 3

since tan30=1/√3

A = 30 

given C = 90 .... so, A + B + C = 180

                         or,  B = 60

also tanb=√3

and tan60=√3

           B=60

Now, sinA.cosB + cosA.sinB = sin ( A + B ) = sin ( 30 + 60 ) = sin 90 = 1

so your answer is 1