Question

чему равен sin105° ?
2. докажите, что верно равенство (sinx+cosx)²=1+sin2x

Answer 1

Sina+cosa=sin^2+2siacosa+cos^2= 1+sin2a

Answer 2

$sin(105^{circ})=sin(180^{circ}-75^{circ})=sin(75^{circ})=sin(45^{circ}+30^{circ})=\=sin(45^{circ})*cos(30^{circ})+sin(30^{circ})*cos(45^{circ})= frac{sqrt{2}}{2}( frac{sqrt{3}}{2} + frac{1}{2} )=\=frac{sqrt{2}}{2}* frac{sqrt{3}+1}{2} = frac{sqrt{2}(sqrt{3}+1)}{4}$
Ответ: г
$(sinx+cosx)^2=1+sin2x \sin^2+2sinxcosx+cos^2x=1+sin2x \(sin^2x+cos^2x)+2sinx*cosx=1+sin2x \1+sin2x=1+sin2x$