How can I demonstrate that (sin(T)+cos(T))(1-sin(T)cos(T))=(sin(T))^3+(cos(T))^3
You first develop the expression on the left side of the equation:(sin(T)+cos(T))(1-sin(T)cos(T))=sin(T)-sin^2(T)cos(T)+cos(T)-sin(T)cos^2(T)=sin(T)(1-cos^2(T))+cos(T)(1-sin^2(T))Now, you will need to use the formula cos^2(T)+sin^2(T)=1Hence, 1-cos^2(T)=sin^2(T) and 1-sin^2(T)=cos^2(T)You now have the following equation: (sin(T)+cos(T))(1-sin(T)cos(T))=sin(T)(sin^2(T))+cos(T)(cos^2(T))QED
TC
Related Maths A Level answers
All answers ▸find the derivative of f(x) = x^3 + 2x^2 - 5x - 6. Find all stationary points of the function.
Calculate the volume obtained when rotating the curve y=x^2 360 degrees around the x axis for 0<x<2
Solve the simultaneous equations: y + 4x + 1 = 0, and y^2 + 5x^2 + 2x = 0.
Find the equation of the tangent to the curve y = 3x^2 + 4 at x = 2 in the form y = mx + c