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.