Bài 64 trang 219 Đại số 10 Nâng cao: Chọn đáp án đúng:...

$\sin {{{{90}^0}} \over 4}\cos {{{{270}^0}} \over 4}$ bằng: 

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

Đáp án

Ta có:

 $\sin {{{{90}^0}} \over 4}\cos {{{{270}^0}} \over 4} = {1 \over 2}\sin ({90^0} - \sin {45^0})$

$= {1 \over 2}(1 - {{\sqrt 2 } \over 2})$

Chọn (A)