Prove: $tan 20^{o} + tan 25^{o} + tan 20^{o} tan 25^{o} = 1$ .

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Solution

As we know that
$tan 45^{\circ} = tan (20^{\circ} + 25^{\circ}) = \frac{tan 20^{\circ} + tan 25^{\circ}}{1 - tan 20^{\circ} tan 25^{\circ}}$
$⟹ \frac{tan 20^{\circ} + tan 25^{\circ}}{1 - tan 20^{\circ} tan 25^{\circ}} = 1$
$⟹ tan 20^{\circ} + tan 25^{\circ} = 1 - tan 20^{\circ} tan 25^{\circ}$
$⟹ tan 20^{\circ} + tan 25^{\circ} + tan 20^{\circ} tan 25^{\circ} = 1$

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