Задание 1. Упрости выражение: 1. sin(90° − α) + sin(90° + α) = 2. cos(90° − α) − cos(90° + α) = 3. sin(180° − α) · cos(180° + α) = 4. sin(180° + α) + cos(180° − α) = 5. cos(90° + α) · sin(180° − α) =

Question

Вопрос:

Accepted Answer

\(\sin(90^\circ-\alpha)+\sin(90^\circ+\alpha)=\cos\alpha+\cos\alpha=2\cos\alpha\).
\(\cos(90^\circ-\alpha)-\cos(90^\circ+\alpha)=\sin\alpha-(-\sin\alpha)=2\sin\alpha\).
\(\sin(180^\circ-\alpha)\cdot\cos(180^\circ+\alpha)=\sin\alpha\cdot(-\cos\alpha)=-\sin\alpha\cos\alpha\).
\(\sin(180^\circ+\alpha)+\cos(180^\circ-\alpha)=-\sin\alpha+(-\cos\alpha)=-(\sin\alpha+\cos\alpha)\).
\(\cos(90^\circ+\alpha)\cdot\sin(180^\circ-\alpha)=(-\sin\alpha)\cdot\sin\alpha=-\sin^2\alpha\).

Ответ: 1) \(2\cos\alpha\); 2) \(2\sin\alpha\); 3) \(-\sin\alpha\cos\alpha\); 4) \(-\sin\alpha-\cos\alpha\); 5) \(-\sin^2\alpha\).