Question

Trig.....need help!! If sinA-cosA=1 then, sin^3 A- cos^3 A is?

Answer 1

\[\Large \sin(A) - \cos(A) = 1\]
\[\Large (\sin(A) - \cos(A))^2 = 1^2\]
\[\Large \sin^2(A) -2\sin(A)\cos(A) + \cos^2(A) = 1\]
\[\Large \sin^2(A) + \cos^2(A) -2\sin(A)\cos(A) = 1\]
\[\Large 1 -2\sin(A)\cos(A) = 1\]
\[\Large -2\sin(A)\cos(A) = 0\]
\[\Large \sin(A)\cos(A) = 0\]

Answer 2

\[x^3 - y^3 = (x-y)*(x^2+xy+y^2)\]
\[\sin^3(A) - \cos^3(A) = (\sin(A) - \cos(A))*(\sin^2(A) + \sin(A)\cos(A) + \cos^2(A))\]
\[\sin^3(A) - \cos^3(A) = (\sin(A) - \cos(A))*(\sin^2(A)+\cos^2(A) + \sin(A)\cos(A))\]
\[\sin^3(A) - \cos^3(A) = (\sin(A) - \cos(A))*(1 + \sin(A)\cos(A))\]
\[\sin^3(A) - \cos^3(A) = (1)*(1 + 0)\]
\[\sin^3(A) - \cos^3(A) = 1\]

Answer 3

Thnx