Use the addition formulas: sin(x+y)=sin(x)*cos(y)+sin(y)*cos(x), cos(x+y)=cos(x)*cos(y)-sin(x)*sin(y) to derive sin(2x), cos(2x), sin(x)+sin(y).

sin(2x)=sin(x+x) =sin(x)cos(x)+cos(x)sin(x) =2*sin(x)*cos(x); cos(2x)=cos(x+x) =cos(x)cos(x)-sin(x)sin(x) =[cos(x)]2-[sin(x)]2 Now let x+y=a and x-y=b, then x=(a+b)/2 and y=(a-b)/2. Then sin(a)=sin[(a+b)/2+(a-b)/2] =sin([a+b)/2]*cos[(a-b)/2]+sin[(a-b)/2]*cos[(a+b)/2]; sin(b)=sin[(a+b)/2+(b-a)/2] =sin[(a+b)/2]*cos[(b-a)/2]+sin[(b-a)/2]*cos[(a+b)/2]; sin(x) is an odd function: sin(x)=-sin(-x) and cos(x) is an even function: cos(x)=cos(-x).Hence, sin(b)=sin([a+b)/2]*cos[(a-b)/2]-sin[(a-b)/2]cos[(a+b)/2]. Adding these two formulas gives: sin(a)+sin(b)=2sin[(a+b)/2]*cos[(a-b)/2]

IS
Answered by Ioana S. Maths tutor

3534 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Define the derivative of a function f(x) and use this to calculate the derivative of f(x)=x^n for positive integer n.


The quadratic equation x^2 + 4kx+2(k+1) = 0 has equal roots, find the possible values of k.


Differentiate (2^x)(5x^2+5x)^2.


How would you differentiate ln(sin(3x))?


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