Question

evaluate=tan85degree -tan40degree /1+tan 85-tan40degree​

Answer 1

Given,

$\Large {\frac{ \tan 85 ^ \circ - \, \tan 40 ^ \circ}{1\, +\, \tan 85 ^ \circ \tan 40 ^ \circ}}$

Using the identity,

$tan(A-B) = \frac{(tanA\, -\, tanB)}{(1\,+\,tanAtanB)}$

We get,

${\frac{ \tan 85 ^ \circ - \, \tan 40 ^ \circ}{1\, +\, \tan 85 ^ \circ \tan 40 ^ \circ}}\\\\= tan(85 ^ \circ - \, 40 ^ \circ) \\= tan(45 ^ \circ) \\= 1 [\,\because tan(45 ^ \circ) = 1]$

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