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

Answered by Tabea C. Maths tutor

2759 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find the area between the curves y = x^2 and y = 4x - x^2.


Find the derivative of sinx, use that to find the derivative of xsinx


Using the equation cos(a+b) = cos(a)cos(b) - sin(a)sin(b) or otherwise, show that cos(2x) = 2cos^2(x) - 1.


Can you prove to me why cos^2(X) + sin^2(X) = 1?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences