Question

If A and B are acute angles and tanA=1 sinB=1/root2 then the value of cos (A+B) is

Answer 1

tanA=1 can be written as tanA=tan45 tan will cancel. on both side A=45 in the same manner sinB=1÷root2 can be written as sinB=sin45 sin will cancel on both side B=45 now cos(A+B)=cos(45+45) you will get cos(90) which is equal to zero

Answer 2

Tan A = 1 -(1)
also Tan 45 =1 -(2)
equating (1)&(2)
Tan A= Tan 45
=A=45 degrees
similarly sin 45 is equal to 1/ root 2.
so B=45.
cos (A+B )= cos 90
=0