Cho sinα = 12/13 và cosα =-5/13 . Tính sin( -15 bi /2- anpha)-cos ( 13 bi +anpha).

Trả lời

Ta có: $\sin \left(-\frac{15\pi }{2}-\alpha \right)-\text{cos}\left(13\pi +\alpha \right)$

$=\sin \left(-\frac{16\pi }{2}+\frac{\pi }{2}-\alpha \right)-\text{cos}\left(12\pi +\pi +\alpha \right)$

$=\sin \left(\frac{\pi }{2}-\alpha \right)-\text{cos}\left(\pi +\alpha \right)$

$=\text{cos}\alpha +\text{cos}\alpha$

$=2\text{cos}\alpha$

$=2.\left(-\frac{5}{13}\right)=-\frac{10}{13}$.