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 ▸The point P lies on a curve with equation: x=(4y-sin2y)^2. (i) Given P has coordinates (x, pi/2) find x. (ii) The tangent to the curve at P cuts the y-axis at the point A. Use calculus to find the coordinates of the point A.
The curve C has equation y = x^3 - 3x^2 - 9x + 14. Find the co-ordinates and nature of each of the stationery points of C.
A cubic polynomial has the form p(z)=z^3+bz^2+cz+d, z is Complex and b, c, d are Real. Given that a solution of p(z)=0 is z1=3-2i and that p(-2)=0, find the values of b, c and d.
How do you integrate ln(x)