103 Trigonometry Problems

5. Solutions to Advanced Problems 159
By the difference-to-product formulas, it follows that
sin 3α + sin 3γ − cos(β − α) − cos(β − γ)
= (sin α − sin γ)(cos 2α − cos 2γ)
+ (cos α − cos γ)(sin 2α − sin 2γ)
= (sin α − sin γ)(cos 2α − cos 2γ)
+ 2(cos α − cos γ)cos(α + γ)sin(α − γ).
Note that sin x is increasing, and cos x and cos 2x are decreasing for 0 ◦