2
If tanA = 1/2 and tanB = 1/3, then what is the value of tan(2A + B)?
- A1
- B3
- C5
- D9
Answer not set
Discussion 1
Log in or create a free account to reply and vote.
0
CCommunity
We know that
tan(A + B) = [(tanA + tanB)/1 - tanAtanB]
So, tan(2A + B) = [(tan2A +tanB)/1 - tan2AtanB]
Also, tan2A = 2tanA/(1 – tan2A)
⇒ tan2A = 2(1/2)/(1 – (1/2)2)
⇒ tan2A = 4/3
⇒ tan(2A + B) = [(4/3 + 1/3)/1 - (4/3)(1/3)]
⇒ tan(2A + B) = (5/3)/(5/9) = 3
⇒ tan(2A + B) = 3
∴ the correct option is 2)
tan(A + B) = [(tanA + tanB)/1 - tanAtanB]
So, tan(2A + B) = [(tan2A +tanB)/1 - tan2AtanB]
Also, tan2A = 2tanA/(1 – tan2A)
⇒ tan2A = 2(1/2)/(1 – (1/2)2)
⇒ tan2A = 4/3
⇒ tan(2A + B) = [(4/3 + 1/3)/1 - (4/3)(1/3)]
⇒ tan(2A + B) = (5/3)/(5/9) = 3
⇒ tan(2A + B) = 3
∴ the correct option is 2)