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Demonstrati : tg(pi/8+x)×tg(pi/8-x)+tg(pi/8+x)+tg(pi/8-x)=1

Răspuns :

Răspuns:

Explicație pas cu pas:

tg (a+b)=tga+tg b/1-tgatgb

tg (π/8+x)+tg(π/8-x)=tg (π/8+x+π/8-x) - tg (π/8+x+π/8-x)tg (π/8+x)tg(π/8-x)

tg (π/8+x+π/8-x)=tg π/4=1

expresia initiala devine

tg (π/8+x)(tgπ/8-x)+1-tg(π/8+x)tg(π/8-x)=1

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