Question

if sinA=1/root2 and cot B=1 then prove that sin (A+B)=1

Answer 1

sinA=1/√2, sinA=sin45°, A=45°
cotB=1, coB=cot45°, B=45°

sin(A+B) = sin(45°+45°) = sin90°= 1

Answer 2

as SinA=1/root2,A=45°
in the same way CotB=1,B=45°
Sin(A+B)=SinACosB+CosASinB
By substituting the values of A and B in the above formula,we get
Sin(45°+45°)=sin45cos45+cos45sin45
sin(90°)=1/√2×1/√2+1/√2+1/√2
1=1/2+1/2
1=1
hence proved