「大学受験数学 三角関数/公式集」の版間の差分

<math>\tan (\alpha\pm\beta)=\frac{\tan \alpha \pm \tan \beta}{1 \mp \tan \alpha\ \tan \beta}</math><br>

 

<math>\sin 15^\circ=\sin (45^\circ-30^\circ)=\sin 45^\circ \cos 30^\circ - \cos 45^\circ \sin 30^\circ=\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2}-\frac{\sqrt{2}}{2} \cdot \frac{1}{2}=\frac{\sqrt{6}-\sqrt{2}}{4}</math><br>

<math>\cos 15^\circ=\cos (45^\circ-30^\circ)=\cos 45^\circ \cos 30^\circ + \sin 45^\circ \sin 30^\circ=\frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2} \cdot \frac{1}{2}=\frac{\sqrt{6}+\sqrt{2}}{4}</math><br>

<math>\tan 2\alpha=\frac{2\tan \alpha}{1-\tan^2 \alpha}</math><br>

 

<math>\sin 2\alpha=\sin (\alpha+\alpha)=\sin \alpha \cos \alpha + \cos \alpha \sin \alpha=2\sin \alpha \cos \alpha</math><br>

<math>\cos 2\alpha=\cos (\alpha+\alpha)=\cos \alpha \cos \alpha - \sin \alpha \sin \alpha=\cos^2 \alpha - \sin^2 \alpha</math><br>

 

 

<math>\cos 2\alpha=1 - 2\sin^2 \alpha</math><br>

<math>2\sin^2 \alpha=1 - \cos 2\alpha</math><br>

<math>\cos \alpha - \cos \beta=-2\sin \frac{\alpha+\beta}{2} \sin \frac{\alpha-\beta}{2}</math><br>

 

 

== 積和変換公式 ==

<math>\cos\alpha\ \cos\beta=\frac{1}{2} \{\cos (\alpha+\beta) + \cos (\alpha-\beta)\}</math><br>

 

 

== 三倍角の公式 ==

 

 

 

<math>\sin 3\alpha=\sin(\alpha +2 \alpha)</math><br>

<math>cos^3 \alpha=\frac{1}{4}(3\cos \alpha + \cos 3\alpha)</math><br>

 

<math>\sin 3\alpha=-4sin^3 \alpha + 3\sin \alpha</math><br>

<math>\sin 3\alpha - 3\sin \alpha=-4sin^3 \alpha</math><br>