Question

Tính

S= cos⁶ 5° + sin⁶ 5°-3/8 sin70°

Answer 1

\(cos^6x+sin^6x=\left(cos^2x+sin^2x\right)^3-3sin^2x.cos^2x\left(sin^2x+cos^2x\right)\)

\(=1-3sin^2x.cos^2x=1-\frac{3}{4}sin^22x\)

\(=1-\frac{3}{8}\left(1-cos4x\right)=\frac{5}{8}+\frac{3}{8}cos4x\)

\(\Rightarrow S=cos^65+sin^65-\frac{3}{8}sin70\)

\(=\frac{5}{8}+\frac{3}{8}cos20-\frac{3}{8}sin\left(90-20\right)\)

\(=\frac{5}{8}+\frac{3}{8}cos20-\frac{3}{8}cos20=\frac{5}{8}\)