If tan-1tan5π4=α and tan-1-tan2π3=β then
4α-4β=0
4α-3β=0
α>β
None of these
Explanation for the correct option:
Step 1: Calculate the value of α
Let, tan-1tanx=x
∴α=tan-1tan5π4=tan-1tanπ+π4=tan-1tanπ4=π4
∴4α=π...(1)
Step 2 : Calculate the value of β
∵β=tan-1-tan2π3=tan-1-tanπ-π3=tan-1tanπ3=π3
∴3β=π...(2)
Step 3: Equating the equation (1) and (2)
∴π=π⇒4α=3β
Hence option (B) is correct
If α + β = 90o and α : β = 2 : 1, then, sin α : sin β =