Question

write the following function in terms of its cofunction. assume that all angles in which an unknown appears are acute angles. sec (β + 15°) sec (β + 15°)= (simplify your answer. do not include the degree symbol in your answer.)

Explanation:

Step1: Recall co - function identity

The co - function identity for secant and cosecant is $\sec\theta=\csc(90 - \theta)$.
Let $\theta=\beta + 15$.

Step2: Apply the co - function identity

We substitute $\theta$ into the identity: $\sec(\beta + 15)=\csc(90-(\beta + 15))$.

Step3: Simplify the expression

Expand $90-(\beta + 15)$: $90-(\beta + 15)=90-\beta - 15=75-\beta$. So, $\sec(\beta + 15)=\csc(75-\beta)$.

Answer:

$\csc(75 - \beta)$