Question:
Prove that: $\frac{7 \pi}{12}+\cos \frac{\pi}{12}=\sin \frac{5 \pi}{12}-\sin \frac{\pi}{12}$
Solution:
$105^{\circ}=\frac{7 \pi}{12}, 15^{\circ}=\frac{\pi}{12}, 75^{\circ}=\frac{5 \pi}{12}, 15^{\circ}=\frac{\pi}{12}$
LHS = cos105o + cos15o
= cos(90o + 15o) + cos(90o
= - sin 15o + sin 75o [As cos(90o+A) =
= sin 75o
= RHS
Hence proved.