Question

analyzing cofunctions
consider △lmn.
m∠l + m∠m =
sin(l) =
sin(m) =

Explanation:

Step1: Sum of acute angles in right triangle

In a right triangle, the sum of the two non-right angles is $90^\circ$.
$m\angle L + m\angle M = 42^\circ + 48^\circ = 90^\circ$

Step2: Relate sine to cosine of cofunction

For complementary angles $\alpha$ and $\beta$ where $\alpha+\beta=90^\circ$, $\sin(\alpha)=\cos(\beta)$.
$\sin(L) = \sin(42^\circ) = \cos(48^\circ) = \cos(M)$

Step3: Identify sine of angle M

$\sin(M) = \sin(48^\circ) = \cos(42^\circ) = \cos(L)$

Answer:

$m\angle L + m\angle M = 90$
$\sin(L) = \cos(M)$
$\sin(M) = \cos(L)$