Question

Use the sum and difference identities to determine the exact value of the following expression. If the answer is undefined, write DNE.cos110 cos25 - sin1 10 sin25

Answer 1

`\cos (135^(\circ))`

1) Considering the sum and difference trig identities, we can rewrite that as the sum of cosines.

2) Therefore, we can rewrite that as the following and then reducing to the equivalent angle (in degrees):

`\begin{gathered} \cos (a+b)=\cos (a)\cos (b)-\sin (a)\sin (b) \\ ---- \\ \cos (110)\cos (25)-\sin (110)\sin (25) \\ \cos (110+25) \\ \cos (135) \end{gathered}`

Note that the sum of cosines yields an expression that has a minus sign between the minuend and subtrahend.