Question

If sin(a+b)=1 and sin(a-b)=1/2 find tan(a+2b)tan(2a+b)

Answer 1

Step-by-step explanation:

sin (a+b)=1

but sin90=1

a+b = 90 (1)

sin(a-b) =1/2

but sin 30 =1/2

a-b=30 (2)

solving (1) and (2)

a=60 b =30

tan (a+2b)= tan(60+2*30)

=tan (150)

=-1/√3

tan (2a+b)= tan (2*30+30)

tan(90)=1/0=undefined