what is the exact value of cos 54* cos 8* + sin 53 * sin 8* *= Degrees

Question

what is the exact value of cos 54* cos 8* + sin 53 * sin 8*    *= Degrees

anonymous · Answer

That looks a lot like a trig identity.. $cos(\theta - \phi)$ probably.

anonymous · Answer

Well where doing functions of the sum of two angles... if that means anything Trigonnometric applications. of some sort and i know the chart is involved with the 30 45 60  sin , cos, tan kinda thing what is the thing next to beta.?

anonymous · Answer

Yeah, if you look in your book, or your notes you should see a formula that looks like this one except without the numbers. The formula you have here is the one for the sum/difference of two angles for cosine. 

$$cos(\theta \pm \phi) = cos(\theta)cos(\phi) \mp sin(\theta)sin(\phi)$$

In this case, $\theta=53$ and $\phi=8$. Since you are adding the product of the sines to the product of the cosines you just want to take the cosine of the difference between the two. 53-8 = 45. So the answer is the cos of 45 degrees.