Prove that $tan 15^{o} + tan 30^{o} + tan 15^{o} tan 30^{o} = 1$

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Solution

$tan 15^{o} + tan 30^{o} = 1 - tan 15^{o} tan 30^{o}$
or $\frac{tan 15^{o} + tan 30^{o}}{1 - tan 15^{o} tan 30^{o}} = 1$
or $tan (15^{o} + 30^{o}) = 1$
or $tan 45^{o} = 1$ , which is true

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