Express the given product as a sum or difference containing only sines or cosines. sin (8x) cos (4x) sin (8x) cos (4x)= LU (Simplify your answer.)

Please help me, I can't seem to figure it out and it is due in 25 minutes. Someone, please help me ASAP! Thank you!

2x+1 x-1) (x+2) tvaluale followay iolegral

Deriving Snell's Law from an Optimization Problem Refraction is a physical phenomenon that happens when light, or more generally a wave, passes through two different mediums. In this problem, we consider two mediums separated by an horizontal line of length d (for example, this line could separate the water in a pool and the air above it). A photon is emitted from a source placed at a point A and detected at a point B. See Figure 1 for the placement of A and B. First Medium A h₁ d Second Medium B Figure 1: Photon emission and detection points. The speeds of the photon in the first and second medium are v₁ and #2, respectively. The refraction indexes are defined as n₁and n₂ = where c is the speed of light in vacuum. Assuming that the photon travels on the fastest path from A to B, prove Snell's law of refraction sin 01 ปา sin 02 v2 where 01 and 02 are the angles defined in Figure 2. First Medium A d Second Medium B Figure 2: Definition of 1 and 02. (1) Suggested steps: 1. Choose the…

Content ← C Math 1314 HW 1-Section 1.1- X Math 1314-30381- Online, S X ✰ webassign.net/web/Student/Assignment-Responses/submit?dep=29338960&tags-aut 15 5 (6, 0) 10 (11, 0) -5 (a) Find the length of each side of the right triangle. distance between (6, 0) and (11, 0) 91 5 distance between (11, 0) and (11, 12) d2 = 12 distance between (6, 0) and (11, 12) d3 = 13 (b) Show that these lengths satisfy the Pythagorean Theorem. d₁² d₂² 111 2 d₁² + d₂² 225 = d₂² $ IL SARRE 2 3 % 5 Oll 6 T 22