Bài 60 trang 219 Đại số 10 Nâng cao: Chọn đáp án đúng:...

Nếu $\sin \alpha  + \cos \alpha  = {1 \over 2}$ thì sin2α  bằng: 

$\eqalign{ & (A)\,{3 \over 8}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(B)\, - {3 \over 4} \cr & (C)\,{1 \over {\sqrt 2 }}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(D)\,{3 \over 4} \cr}$

Đáp án

Ta có:

$\eqalign{ & \sin \alpha + \cos \alpha = {1 \over 2} \Rightarrow 1 + 2\sin \alpha \cos \alpha = {1 \over 4} \cr & \Rightarrow \sin 2\alpha = - {3 \over 4} \cr}$ 

Chọn (B)