Question

rút gọn và tính giá trị các biểu thức ( k dùng máy tính)

A=\(\cos10^0+\cos40^0+\cos70^0+...+\cos170^0\)

B= \(\sin5^0+\sin10^0+\sin15^0+....+\sin360^0\)

C= \(\cos^22^0+\cos^24^0+\cos^26^0+...+\cos^288^0\)

Answer 1

\(A=cos10+cos170+cos40+cos140+cos70+cos110\)

\(A=cos10+cos\left(180-10\right)+cos40+cos\left(180-40\right)+cos70+cos\left(180-70\right)\)

\(A=cos10-cos10+cos40-cos40+cos70-cos70\)

\(A=0\)

\(B=sin5+sin355+sin10+sin350+...+sin175+sin185+sin360\)

\(B=sin5+sin\left(360-5\right)+sin10+sin\left(360-10\right)+...+sin175+sin\left(360-175\right)+sin360\)

\(B=sin5-sin5+sin10-sin10+...+sin175-sin175+sin360\)

\(B=sin360=0\)

\(C=cos^22+cos^288+cos^24+cos^284+...+cos^244+cos^246\)

\(C=cos^22+cos^2\left(90-2\right)+cos^24+cos^2\left(90-4\right)+...+cos^244+cos^2\left(90-44\right)\)

\(C=cos^22+sin^22+cos^24+sin^24+...+cos^244+sin^244\)

\(C=1+1+...+1\) (có \(\frac{44-2}{2}+1=22\) số 1)

\(\Rightarrow C=22\)