If `sin A = 1/sqrt (3)` and `sin B = 1/sqrt (5)` find the value of `tan ( (A+B)/2).cot ( (A-B)/2)`

If sin A = (1)/(sqrt3) and sin B = (1)/(sqrt5) find the value of tan ""(1)/(2) (A + B) . Cot "" (1)/(2) (A-B).

If tan (A-B) = (1)/(sqrt3) and sin A = (1)/(sqrt2) find the value of B.

If sin A= 1/sqrt2 " and" sinB = 1/sqrt3,"find the value of " "tan"(A+B)/2 "cot" (A-B)/2

If sin A = sqrt(3)/2 find the value of 2 cot^(2) A-1 .

If sin A=sqrt3/2 and cos B = sqrt3/2 , find the value of : (tanA-tanB)/(1+tanAtanB)

If tan(A+B)=sqrt(3)andsin(A-B)=(1)/(2) ,then find the value of tan (2A-3B) .

If sin A=(1)/(sqrt(5)) and sin B=(1)/(sqrt(10)) ,find the values of cos A and cos B .Hence using the formula cos(A+B)=cos A cos B-sin A sin B, show that (A+B)=45^(@).

If sin(A+B)=1 and tan(A-B)=1/sqrt(3) , find the value of: (i) tan A + cot B (ii) secA-cosec B

If sin(A+B) =1 and tan(A-B) =1/(sqrt(3)) , 0^@ltA,Blt90^@ , find the value of : tan A+ cot B

If sin (A+B)=1 and cos (A-B) = (sqrt(3))/(2) , find A and B.