R addition formulae Rcos Rsin etc (CIE A Level Maths: Pure 3)

How can I simplify expressions like a sin x ± b cos x  or a cos x ± b sin x?

• If a and b are positive constants, then
  • a sin x + bcos x can be rewritten as R sin (x + α)
  • a sin x - bcos x can be rewritten as R sin (x - α)
  • a cos x + bsin x can be rewritten as R cos (x - α)
  • a cos x - bsin x can be rewritten as R cos (x + α)
• In all four cases R > 0 and 0 < α < 90°, with:

• To rewrite the expression use the appropriate compound angle formula and equate coefficients