Loading…
Reference: Pearson Edexcel International A Level Pure Mathematics 3 Student Book. This chapter gives formulae that let you rewrite trig expressions and solve harder equations.
Main skills from this lesson
The key formulae are:
sin(A + B) = sin A cos B + cos A sin B
sin(A - B) = sin A cos B - cos A sin B
cos(A + B) = cos A cos B - sin A sin B
cos(A - B) = cos A cos B + sin A sin B
Notice the sign pattern carefully.
Cos(A + B) has the minus sign. This is a common exam mistake.
Set A = B to get double-angle formulae.
Choose the version that matches the expression in front of you.
Choose formula by what you want to remove.
Expressions like a cos x + b sin x can be rewritten as R cos(x - alpha) or R sin(x + alpha). This helps solve equations and find maximum/minimum values.
R = sqrt(a^2 + b^2)
Then compare coefficients to find alpha.
a cos x + b sin x = R cos(x - alpha)
After rewriting, the maximum is R and the minimum is -R.
A tidy identity proof usually starts with the more complicated side.
Study routine:
Continue with quizzes, flashcards, or games when you are ready.