Question

求大神帮我解决几道数学题

Answer 1

1等腰直角△，因sinB>0,sinC>0,要使(sinB)^2=(sinC)^2,则sinB=sinC,有B=C或B+C=180,而B,C是△的内角，故B=C;
由正弦定理a/sinA=b/sinB=c/sinC=k,代入已知式，ksinBcosC+ksinCcosB=k(sinA)^2,
sin(B+C)=(sinA)^2, sin(180_A)=(sinA)^2,
sinA_(sinA)^2=0, sinA(1_sinA)=0,
sinA=0,或sinA=1,只有sinA=1,即A=90;

追答

2题，根据正弦定理a/sinA=b/sinB=c/sinC=k,
2a^2/k=(2b_c)*b/k+(2c_b)*c/k,
2a^2=2b^2+2c^2_2bc,
a^2=b^2+c^2_bc,
而余弦定理a^2=b^2+c^2_2bccosA,
即有cosA=1/2, A=60;

sinB+sinC=sinB+sin(180_A_B)=sinB+sin(120_B)=sinB+cosB√3/2+sinB/2=3sinB/2+cosB√3/2=√3;
sinB√3/2+cosB/2=1,
sin(B+30)=1,
B+30=90,B=60, C=60,
△为等边△