Final answer:
The student's questions are simplified using trigonometric identities. Cosine difference simplifies part (a) to cos(4), and the tangent sum formula simplifies part (b) to tan(30).
Step-by-step explanation:
The question provided by the student falls under the category of trigonometry, specifically utilizing trigonometric identities to simplify expressions. To address the student's request, we can use the sum and difference formulas for sine and cosine.
Part a)
The expression cos(32)cos(28) - sin(32)sin(28) can be simplified using the cosine difference identity, which states:
cos(α - β) = cos(α)cos(β) + sin(α)sin(β)
By rearranging the terms, we can write:
cos(32 - 28) = cos(32)cos(28) + sin(32)sin(28)
Therefore, cos(32)cos(28) - sin(32)sin(28) = cos(4).
Part b)
Similarly, the expression tan(48) - tan(18)/(1 + tan(48)tan(18)) can be simplified using the tangent sum formula, which is:
tan(α - β) = (tan(α) - tan(β))/(1 + tan(α)tan(β))
Applying this, we get tan(48 - 18) = tan(30).