Question

tan (45° + theta)=1+tan theta/1-tan theta




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Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

We are aware of the Trigonometric identity that

$\displaystyle \: \: tan(A + B) = \frac{tan A + tan B \: }{1 - tan A \: tan B }$

CALCULATION

$\displaystyle \: \: tan( {45}^{ \circ} + \theta \: )$

$= \displaystyle \: \frac{tan {45}^{ \circ} + tan \theta \: }{1 - tan {45}^{ \circ} \: tan \theta }$

$= \displaystyle \: \frac{1 + tan \theta \: }{1 - \: tan \theta } \: \: ( \because \: tan \ {45}^{ \circ} = 1)$