Using trigonometric identities, show that (cos(x) + sin(x))^2=1+sin(2x)

First being by expanding the brackets of the formula on the left:  (cos(x) + sin(x))2 = (cos(x) + sin(x))*(cos(x) + sin(x)) = cos2(x)+2cos(x)sin(x)+sin2(x).Now we must use our understanding of trigonometric identities: remember that cos2(x)+sin2(x)=1 and 2cos(x)sin(x)=sin(2x).Substituting these identities back into the expanded form of the equation, we show that (cos(x) + sin(x))2=1+sin(2x)

Answered by Maths tutor

5015 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Prove that (sinx + cosx)^2 = 1 + 2sinxcosx


Given y =( 2x+1 )^0.5 and limits x = 0 , x = 1.5 , find the exact volume of the solid generated when a full rotation about the x-axis .


Find the set of values of x for which x(x-4) > 12


Solve the


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences