Answer to Question #286290 in Trigonometry for EMILY

Question

If cos(A-B) = cos 15° and cos(A+B)= cos 75° , the values of A and B. Hence without using a calculator and by using the sum and difference formula, show that cos 15° - cos 75° = 2 sin 45° sin 30°

Answer 1

$A = 45^o \space \space B=30^o$

$-\begin{cases} cos(A-B) = cosAcosB+sinAsinB=cos15^o \\ cos(A+B) = cosAcosB-sinAsinB=cos75^o \end{cases}$

$cos15^o-cos75^o=2sinAsinB=2sin45^osin30^o$