First slide

Trigonometric transformations

Question

The value of $\frac{3 + \cot â¡ 76^{â} \cot â¡ 16^{â}}{\cot â¡ 76^{â} + \cot â¡ 16^{â}}$ is

Moderate

A

cot 44Â°
B

cot 46Â°
C

tan 2â
D

cot 92â

Solution

We can write $\frac{4 + \cot â¡ 76^{â} \cot â¡ 16^{â} â 1}{\cot â¡ 76^{â} + \cot â¡ 16^{â}}$
$\begin{array}{l} = \frac{4 \sin â¡ 76^{â} \sin â¡ 16^{â}}{\sin â¡ 92^{â}} + \cot â¡ 92^{â} \\ = \frac{2 (\cos â¡ 60^{â} â \cos â¡ 92^{â}) + \cos â¡ 92^{â}}{\sin â¡ 92^{â}} = \frac{1 â \cos â¡ 92^{â}}{\sin â¡ 92^{â}} \\ = \cot â¡ 46^{â} = \tan â¡ 44^{â} \end{array}$

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