Problema de matemática.Por favor me ajudem...?

bruno · May 2021

Mostre que: tg ( ά + π/4 ) . tg ( ά - π/4 ) = -1 , para ά ≠ π/4 + kπ/2

angelscarolzinha · May 2021

tg(ά + π/4)*tg(ά - π/4) = - 1

[ tg(ά) + tg(π/4) ] / [ 1 - tg(ά)*tg(π/4) ] * [ tg(ά) - tg(π/4) ] / [ 1 + tg(ά)*tg(π/4) ] = - 1

[ tg(ά) + 1] / [ 1 - tg(ά)*1 ] * [ tg(ά) - 1 ] / [ 1 + tg(ά)*1 ] = - 1

[ tg(ά) + 1] / [ tg(ά) + 1] * [ tg(ά) - 1 ] / [ 1 - tg(ά)*1 ] = - 1

1*[tg(ά) - 1]/[1 - tg(ά)] = - 1

[tg(ά) - 1]/(- 1)*[- 1 + tg(ά)*1 ] = - 1

1/(- 1) = - 1

- 1 = - 1

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