value of expression (cos5x + cos3x)/ (sin5x - sin3x) where x = (3.14/8)

Answer 1

what, no calculator?
since sin 5pi/8 = sin 3pi/8, and cos 5pi/8 = -cos 3pi/8, the fraction is 0/0.

So, using l'Hospital's Rule, we get

(-5sin 5pi/8 - 3sin 3pi/8)/(5cos 5pi/8 - 3cos 3pi/8)
= -8sin(3pi/8)/-8cos(3pi/8)
= tan 3pi/8
= 2.4142

Using the approximate value given, we get 2.41557