Sin36°+sin40°+sin44°+sin48°\2sin88°cos4°sin42°

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We can simplify this expression by using the sum-to-product trigonometric identities for sine.

sin36° + sin40° + sin44° + sin48° = 2(sin88°/2)cos(40°+4°)

Using the identity sin(A)cos(B) = (1/2)(sin(A+B) + sin(A-B)), we can rewrite the expression as:

2(sin88°/2)cos(40°+4°)sin42° = 2(sin44°)cos(40°)sin42°
= 2(2sin22°cos22°)cos40°sin42°
= 2sin44°sin20°cos40°sin42°
= 2sin44°sin20°sin50°

Now, applying the identity sinA*sinB = (1/2)(cos(A-B) - cos(A+B)), we have:

2sin44°sin20°sin50° = (1/2)(cos(24°) - cos64°)

Therefore, the simplified expression is:

(1/2)(cos(24°) - cos64°)