Question

Вычислите
2 Sin²α+√2 Cosα+tgα, если ctgα=1 0<α<π/2

Answer 1

$ctga=1; ; ; i; ; ; 0 textless a textless frac{pi}{2}quad Rightarrow quad a=frac{pi}{4}\\2sin^2a+sqrt2cosa+tga=2sin^2frac{pi}{4}+sqrt2cdot cosfrac{pi}{4}+tgfrac{pi}{4}=\\=2cdot (frac{sqrt2}{2})^2+sqrt2cdot frac{sqrt2}{2}+1=1+1+1=3$