Тест по теме: Формулы двойного аргумента

\sin 2x = 2 \sin x \cos x

\cos 2x = \cos^2 x - \sin^2 x.

\sin 2x = \sin (x+x) =

\sin x \cos x + \cos x \sin x =

2 \sin x \cos x.

\cos 2x =

\cos (x+x) =

\cos x \cos x - \sin x \sin x =

\cos^2 x - \sin^2 x.

\operatorname{tg} 2x = \cfrac{2\operatorname{tg} x}{1 - \operatorname{tg}^2 x}.

\operatorname{tg} 2x = \operatorname{tg}(x+x) =

\cfrac{\operatorname{tg} x + \operatorname{tg} x}{1 - \operatorname{tg} x \cdot \operatorname{tg} x} =

\cfrac{2 \operatorname{tg} x}{1 - \operatorname{tg}^2 x}.

\sin 4x = 2 \sin 2x \cos 2x

\cfrac{\sin 2 t}{\cos t}-\sin t

\cfrac{\sin 2 t}{\cos t}-\sin t=

\cfrac{2 \sin t \cos t}{\cos t}-\sin t=

2 \sin t-\sin t=\sin t

\sin x = 2 \sin \cfrac{x}{2} \cos \cfrac{x}{2}

\cos 48^\circ = \cos^2 24^\circ - \sin^2 24^\circ

\cfrac{\sin 6 t}{\cos ^2 3 t}=

\cfrac{2 \sin 3 t \cos 3 t}{\cos ^2 3 t}=

\cfrac{2 \sin 3 t}{\cos 3 t}=2 t g 3 t

\cos (2x+6y) = \cos^2(x+3y) - \sin^2(x+3y)

\cos ^2 t-\cos 2 t=

\cos ^2 t-\Big(\cos ^2 t-\sin ^2 t\Big)=

\cos ^2 t-\cos ^2 t+\sin ^2 t=\sin ^2 t

\cfrac{\sin 40^{\circ}}{\sin 20^{\circ}}=

\cfrac{2 \sin 20^{\circ} \cos 20^{\circ}}{\sin 20^{\circ}}=

2 \cos 20^{\circ} \operatorname{tg} 20^{\circ}{n}

\operatorname{tg} \Big(\cfrac{2\pi}{3} - 2t\Big) = \cfrac{2 \operatorname{tg} \Big(\cfrac{\pi}{3} - t\Big)}{1 - \operatorname{tg}^2 \Big(\cfrac{\pi}{3} - t\Big)}.

\cfrac{\sin 100^{\circ}}{2 \cos 50^{\circ}}=

\cfrac{2 \sin 50^{\circ} \cos 50^{\circ}}{2 \cos 50^{\circ}}=

\sin 50^{\circ} \operatorname{tg} 50^{\circ}{n}

2 \sin 15^{\circ} \cos 15^{\circ}=

\sin 30^{\circ}=\sin \cfrac{\pi}{6}=\cfrac{1}{2}

\cos 30^{\circ}{n}

\cos ^2 15^{\circ}-\sin ^2 15^{\circ}=

\cos 30^{\circ}=\cfrac{\sqrt{3}}{2}

\sin 30^{\circ}{n}\sqrt{2}{n}