First slide

Compound angles

Question

In an acute angled triangle $\cot A \cot B + \cot C \cot A + \cot B \cot C =$

Easy

A

4
B

1
C

0
D

$\frac{1}{2}$

Solution

We have
$\begin{array}{l} A + B + C = π \\ \Rightarrow A + B = π - C \end{array}$
$\begin{array}{l} \Rightarrow \cot (A + B) = c o t (π - C) \\ \Rightarrow \cot (A + B) = - \cot C \\ \Rightarrow \frac{\cot A \cot B - 1}{\cot B + \cot A} = - \cot C \\ \Rightarrow - \cot B \cot C - \cot A \cot C = \cot A \cot B - 1 \\ \Rightarrow \cot A \cot B + \cot B \cot C + \cot C \cot A = 1 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App