已知a是锐角,且sin(A减四分之派）等于五根号五,求SinA

网友回答

根据A是锐角,那么A∈(0,π/2)
所以A-π/4∈(-π/4,π/4)
另外根据sin(A-π/4)=√5/5>0所以A-π/4∈(0,π/4)
所以 cos(A-π/4)=2√5/5
所以sinA=sin(A-π/4+π/4)
=sin(A-π/4)cos(π/4)+cos(A-π/4)sinπ/4
=(√5/5)(√2/2)+(2√5/5)(√2/2)
=3√10/10