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$\tan 100^{0} + \tan 125^{0} + \tan 100^{0} \tan 125^{0} =$

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Detailed Solution

$100^{0} + 125^{0} = 225^{0} \tan (100 + 125) = \tan 225 \frac{\tan 100 + \tan 125}{1 - \tan 100 \tan 125} = \tan 225$

$\tan 225^{0} - \tan 100^{0} - \tan 125^{0} = \tan 225^{0} \tan 100^{0} \tan 125^{0}$

$\Rightarrow \tan 100^{0} + \tan 125^{0} + \tan 100^{0} \tan 125^{0} = 1$

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