Solve the expression e sina cos a sin2a cos2a if cos a

Solve the expression e = sina + cos a + sin2a + cos2a if cos a = -1/4 belongs to (pi, 3pi/2).

e = sina+cosa+sin2a+cos2a +cos2a cosa= -1/4 and is in (pi,3i/2).

Both sin and cos ratios are negative for angles in 3rd quadrant.

We know sina = - sqrt(1-1/4^2) = -sqrt15/4.

sin2a = 2sinacos = 2(-1/4)(-sqr15/4) = (sqrt15)/4

cos2a = 2so^2a -1 = 2(-1/4)^2-1 = 1/8 -1 = -7/8.

Substituting in the given expression the values, we get:

Therefore e = -(sqrt15)/4 -1/4 +(sqrt15)/4 -7/8 = -1/4-7/8 = -9/4.

Therefore e = -9/4