First slide

Compound angles

Question

tan 100° + tan 125° + tan 100° tan 125° is equal to

Easy

A

0
B

1 /2
C

-1
D

1

Solution

$\begin{array}{l} \tan (100^{\circ} + 125^{\circ}) = \frac{\tan 100^{\circ} + \tan 125^{\circ}}{1 - \tan 100^{\circ} \tan 125^{\circ}} \\ ∴ \tan 225^{\circ} = \frac{\tan 100^{\circ} + \tan 125^{\circ}}{1 - \tan 100^{\circ} \tan 125^{\circ}} \\ i . e ., 1 = \frac{\tan 100^{\circ} + \tan 125^{\circ}}{1 - \tan 100^{\circ} \tan 125^{\circ}} \end{array}$
i.e., tan100° + tan 125° + tan 100° tan 125° = 1

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