Question

Вычислите: tg²15⁰ + ctg²15⁰

Answer 1

Ответ:

14.

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Answer 2

$1+tg^{2}15^{0}=\frac{1}{Cos^{2}15^{0}}\Rightarrow tg^{2}15^{0}=\frac{1}{Cos^{2}15^{0}}-1\\\\1+Ctg^{2}15^{0}=\frac{1}{Sin^{2}15^{0}}\Rightarrow Ctg^{2}15^{0}=\frac{1}{Sin^{2} 15^{0}}-1 \\\\\\tg^{2}15^{0}+Ctg^{2}15^{0}=\frac{1}{Cos^{2}15^{0}}-1+\frac{1}{Sin^{2}15^{0}}-1=\frac{Sin^{2}15^{0}+Cos^{2}15^{0}}{Sin^{2}15^{0}*Cos^{2}15^{0}}-2=\frac{1}{Sin^{2}15^{0}*Cos^{2}15^{0}}-2=\frac{1*4}{4*Sin^{2}15^{0}*Cos^{2}15^{0}}-2=\frac{4}{Sin^{2}30^{0}}-2=\frac{4}{(\frac{1}{2})^{2}}-2=16-2=14$