Question

If sin A+B=1 and tan A-B= 1 root 3 find the value of tan A+cotB

Answer 1

Sec(A+B)=1
(A+B)=90 degree ------(1)
tan(A-B)=1/√3
(A-B)=30degree-----(2)
Solving (1) and (2) we get,
A=60degree
B=30degree
1)tanA+cotB
tan 60degree+cot 30degree
√3+√3=2√3
2)secA-cosB
sec 60degree-cosec 30degree
2-2=0

Answer 2

From the given equation, Sin(A+B)=1 Or,Sin(A+B) =Sinπ/2 Or, A+B=π/2.----------(1) Again, tan(A-B) =1/√3 Or, tan(A-B)=tanπ/6 Or, A-B=π/6------------(2) By adding the equation( 1 )and( 2) we get, 2A=π/2+π/6 Or, 2A=4π/6 Or, A=π/3 and putting the value of A in the equation (1) we get B=π/2-π/3=π/6. Hence, the value of tanπ/3+cotπ/6=2√3