Question

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

Explanation:

Step1: Recall angle - sum property of a right - triangle

In right - triangle $\triangle LMN$ with $\angle N = 90^{\circ}$, by the angle - sum property of a triangle ($m\angle L+m\angle M + m\angle N=180^{\circ}$), substituting $m\angle N = 90^{\circ}$, we get $m\angle L + m\angle M=90^{\circ}$.

Step2: Recall co - function identity

The co - function identity states that $\sin\theta=\cos(90^{\circ}-\theta)$. Since $m\angle L + m\angle M = 90^{\circ}$, then $m\angle M=90^{\circ}-m\angle L$ and $\sin(L)=\cos(M)$. Also, $m\angle L = 90^{\circ}-m\angle M$, so $\sin(M)=\cos(L)$.

Answer:

$\cos(L)$