Question

Aratati ca tg²60° + tg²45°=4

Answer 1

Sinus de 30° = [tex] \frac{1}{2} [/tex]

Sinus de 45° = $\frac{ \sqrt{2} {2}$

Sinus de 60° = $\frac{ \sqrt{3} {2}$

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Cosinus de 30° = $\frac{ \sqrt{3} {2}$

Cosinus de 45° = $\frac{ \sqrt{2} {2}$

Cosinus de 60° = $\frac{1}{2}$

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Tangenta de 30° = $\frac{ \sqrt{3} {3}$

Tangenta de 45° = 1

Tangenta de 60° = $\sqrt{3}$

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Cotangenta de 30° = $\sqrt{3}$

Cotangenta de 45° = 1

Cotangenta de 60° = $\frac{ \sqrt{3} {3}$

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Prin urmare...

tg²60° + tg²45° = $\sqrt{3} ^{2}$ +1² 
Oricare ar fi $\sqrt{x} ^{2}$ rezultat este acel numar "x".

deci,

$\sqrt{3} ^{2}$ +1² = 3 + 1 = 4