Question

If A, B, C are the angles of a non right angled triangle ABC, Then the value of $\left| \begin{matrix} \tan A & 1 & 1 \\ 1 & \tan B & 1 \\ 1 & 1 & \tan C \end{matrix} \right|$ is equal to –

• A. 1
• B. 2
• C. –2
• D. –1

Answer 1

Answer: (B)

2

Answer 2

∆ = tanA(tanB tanC – 1) + (1 – tanC) + (1 – tanB)

= 2 + tanAtanBtanC – (tanA + tanB + tanC)

=2 [Q In ∆ABC, tanA + tanB + tanC = tanA tanB tanC]