Question

(cos20+cos70)^2-sin40

Answer 1

$(cos20+cos70)^2-sin40=[\; cos70=cos(90-20)=sin20\; ]=\\\\=(cos20+sin20)^2-sin40=\\\\=cos^220+\underbrace {2\, sin20\, cos20}_{sin40}+sin^220-sin40=\\\\=(\underbrace {cos^220+sin^220}_{1})+sin40-sin40=1$