sin^2(270)-cos^2(270)+tan^2(60)

解

sin^{2} (27 0^{\circ}) - cos^{2} (27 0^{\circ}) + tan^{2} (6 0^{\circ})

sin^{2} (\frac{3 π}{2}) - cos^{2} (\frac{3 π}{2}) + tan^{2} (\frac{π}{3})

十進法表記

4

解答ステップ

sin^{2} (27 0^{\circ}) - cos^{2} (27 0^{\circ}) + tan^{2} (6 0^{\circ})

三角関数の公式を使用して書き換える:

- cos^{2} (27 0^{\circ}) + sin^{2} (27 0^{\circ}) = - cos (18 0^{\circ})

- cos^{2} (27 0^{\circ}) + sin^{2} (27 0^{\circ})

2倍角の公式を使用:

cos^{2} (x) - sin^{2} (x) = cos (2 x)

- cos^{2} (x) + sin^{2} (x) = - cos (2 x)

= - cos (2 \cdot 27 0^{\circ})

簡素化

= - cos (54 0^{\circ})

cos (54 0^{\circ}) = cos (18 0^{\circ})

cos (54 0^{\circ})

54 0^{\circ}

を書き換え

36 0^{\circ} + 18 0^{\circ}

= cos (36 0^{\circ} + 18 0^{\circ})

以下の周期性を適用する:

cos

cos (x + 36 0^{\circ}) = cos (x)

cos (36 0^{\circ} + 18 0^{\circ}) = cos (18 0^{\circ})

= cos (18 0^{\circ})

= - cos (18 0^{\circ})

= sin^{2} (27 0^{\circ}) - cos^{2} (27 0^{\circ}) + tan^{2} (6 0^{\circ})