Question

Qual o valor de (tan 10◦ + cot 10◦ ) · sin 20◦ ?

Answer 1

$\sf \: ( \tan(10°) + \cot(10°) ) \times \sin(20°) \\ \sf \: \Bigg( \frac{ \sin(10°) }{ \cos(10°) } + \cot(10°) \Bigg) \times \sin(20°) \\ \sf \: \Bigg( \frac{ \sin(10°) }{ \cos(10°) } + \frac{ \cos(10°) }{ \sin(10°) } \Bigg) \times \sin(20°) \\ \sf \: \Bigg( \frac{ \sin(10°) }{ \cos(10°) } + \frac{ \cos(10°) }{ \sin(10°) } \Bigg) \times 2 \sin(10°) \cos(10°) \\\sf \: 2 \times \frac{ \sin(10°) }{ \cos(10°) } \times \sin(10°) \cos(10°) + 2 \times \frac{ \cos(10°) }{ \sin(10° ) } \times \sin(10°) \cos(10°) \\ \sf \: 2 \sin(10°) \sin(10°) + 2 \times \frac{ \cos(10°) }{ \sin(10°) } \times \sin(10°) \cos(10°) \\ \sf \: 2 \sin(10°) \sin(10°) + 2 \cos(10°) \cos(10°) \\ \sf \: 2 \sin(10°) {}^{2} + 2 \cos(10°) {}^{2} \\\sf \: 2\Bigg( \sin(10° ) {}^{2} + \cos(10°) {}^{2} \Bigg) \\ \sf \: 2 \times 1 \\ \sf \: 2$

Att: Nerd1990