1. Buktikan bahwa : cos (α+β) + cos (α-β) / sin (α+β) + sin (α-β) =cotan α 2. Buktikan identitas trigonometri berikut. Sin α + sin 3α / cos 3α + cos α = -cotan

Jawab:
1.
 [tex] \frac{cos ( \alpha + \beta ) + cos ( \alpha - \beta )}{sin ( \alpha + \beta ) + sin ( \alpha - \beta ) } = cotan \alpha \\ \frac{cos \alpha cos \beta -sin \alpha sin \beta+cos \alpha cos \beta +sin \alpha sin \beta }{sin \alpha cos \beta +sin \beta cos \alpha +sin \alpha cos \beta -sin \beta cos \alpha }=cotan \alpha \\ \frac{2cos \alpha cos \beta }{2sin \alpha cos \beta } =cotan \alpha \\ \frac{cos \alpha }{sin \alpha } =cotan \alpha [/tex]

=> Terbukti

2.
[tex] \frac{sin \alpha +sin3 \alpha }{cos3 \alpha + cos \alpha} = tan2 \alpha \\ \frac{sin \alpha +3sin \alpha - 4sin ^{3} \alpha }{4cos ^{3} \alpha -3cos \alpha +cos \alpha } =tan 2 \alpha \\ \frac{4sin \alpha -4sin ^{3} \alpha }{4cos ^{3} -2cos \alpha } = tan2 \alpha \\ [/tex]

=> Tidak terbukti