Question

M=\(\sin^242^o+\sin^243^o+\sin^244^o+\sin^245^o+\sin^246^o+\sin^247^o+\sin^248^o\) 

Không dung máy tính tính M

Answer 1

Ta có \(\sin x=\cos\left(90^0-x\right)\)

\(\Rightarrow M=\left(\sin^242^0+\sin^248^0\right)+\left(\sin^243^0+\sin^247^0\right)+\left(\sin^244^0+\sin^246^0\right)+\sin^245^0\)

\(=\left(\sin^242^0+\cos^242^0\right)+\left(\sin^243^0+\cos^243^0\right)+\left(\sin^244^0+\cos^244^0\right)+\sin^245^0\)

\(=1+1+1+\left(\frac{\sqrt{2}}{2}\right)^2=3+\frac{1}{2}=\frac{7}{2}\)