How do you prove that $(1 + tan theta)[1 + tan(1/4 pi - theta)] = 2$ ?

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Answer 1 · 2015-02-17T18:31:54

Remembering that:

$tan(alpha-beta)=(tanalpha-tanbeta)/(1+tanalphatanbeta)$ , and

$tan(pi/4)=1$ ,

than:

$(1+tantheta)(1+(tan(pi/4)-tantheta)/(1+tan(pi/4)tantheta))=2rArr$

$(1+tantheta)(1+(1-tantheta)/(1+tantheta))=2rArr$

$(1+tantheta)((1+tantheta+1-tantheta)/(1+tantheta))=2rArr$

$2=2$ , with simply calculations.

How do you prove that (1 + tan theta)[1 + tan(1/4 pi - theta)] = 2(1 + tan theta)[1 + tan(1/4 pi - theta)] = 2?