Question

nalyzing cofunctions consider △lmn. m∠l + m∠m = 90 sin (l) = sin (m) = cos(l) cos(m) cos(n)

Explanation:

Step1: Recall co - function identity

In a right - triangle, if two acute angles \(A\) and \(B\) are complementary (\(A + B=90^{\circ}\)), then \(\sin(A)=\cos(B)\) and \(\sin(B)=\cos(A)\). In right - triangle \(\triangle LMN\) with \(\angle N = 90^{\circ}\), \(\angle L\) and \(\angle M\) are complementary since the sum of the interior angles of a triangle is \(180^{\circ}\), so \(m\angle L+m\angle M = 90^{\circ}\).

Step2: Apply co - function identity for sine and cosine

We know that for complementary angles \(L\) and \(M\) (\(L + M=90^{\circ}\)), \(\sin(L)=\cos(M)\) and \(\sin(M)=\cos(L)\).

Answer:

\(\sin(L)=\cos(M)\)