InterviewSolution
Saved Bookmarks
| 1. |
Prove that:sin \(\cfrac{13\pi}3\) sin \(\cfrac{8\pi}3\) + cos \(\cfrac{2\pi}3\) sin \(\cfrac{5\pi}6\) = \(\cfrac12\) |
|
Answer» LHS = sin \(\cfrac{13\pi}3\) sin \(\cfrac{8\pi}3\) + cos \(\cfrac{2\pi}3\) sin \(\cfrac{5\pi}6\) = sin 780° sin 480° + cos 120° sin 150° = sin (90° × 8 + 60°) sin (90° × 5 + 30°) + cos (90° × 1 + 30°) sin (90° × 1 + 60°) We know that when n is odd, cos → sin and sin → cos. = sin 60° cos 30° + [-sin 30°] cos 60° = sin 60° cos 30° - sin 30° cos 60° We know that sin A cos B – cos A sin B = sin (A – B) = sin (60° - 30°) = sin 30° = 1/2 = RHS Hence proved. |
|