Bài tập Công thức lượng giác

L

lp_qt

$A=sin^220^o+sin^2140^o+sin^2100^o$

$=sin^220^o+sin^240^o+sin^280^o$

$=\dfrac{1-cos40^o}{2}+\dfrac{1-cos80^o}{2}+\dfrac{1-cos160^o}{2}$

$=\dfrac{3}{2}-\dfrac{cos40^o+cos80^o+cos160^o}{2}$

Ta có: $cos40^o+cos80^o+cos160^o=2.cos60^o.cos20^o-cos20^o$

$=cos20^o(2.cos60^o-1)=0$

\Rightarrow $A=\dfrac{3}{2}$

Tính B tương tự
 
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