Quantitative Ability Question of the Day

Consider the equation:

How many solutions to this equation exist for 0° ≤ θ ≤ 360°?

OPTIONS
1) 1
2) 2
3) 3
4) 0


Solution

∴ (log cot θ)2 + (log tan θ)2 – 2(log cot θ)(log tan θ) = 0

∴ (log cot θ – log tan θ)2 = 0

∴ log cot θ = log tan θ, or cot θ = tan θ

 ∴ tan θ = ±1

But log11 and log of a negative number is not defined. So the equation has no solutions.



Hence, option 4.