First slide

Compound angles

Question

If $A + B = 225^{o}$ then the value of $\frac{\cot A}{1 + \cot A} . \frac{\cot B}{1 + \cot B} =$

Easy

A

2
B

1
C

4
D

$\frac{1}{2}$

Solution

$\begin{array}{l} If A + B = 225 ° then (1 + \cot A) (1 + \cot B) = 2 \cot A \cot B \\ ∴ \frac{\cot A \cdot \cot B}{(1 + \cot A) (1 + \cot B)} = \frac{\cot A \cot B}{2 \cot A \cot B} = \frac{1}{2} \end{array}$

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