Question

write the following function in terms of its cofunction. assume that all angles in which an unknown appears are acute angles.
tan (θ + 25°)

tan (θ + 25°) =
(simplify your answer. do not include the degree symbol in your answer.)

Explanation:

Step1: Recall cofunction identity for tangent

The cofunction identity for tangent is $\tan\alpha = \cot(90 - \alpha)$. Here, $\alpha=\theta + 25$.

Step2: Apply the identity

Substitute $\alpha=\theta + 25$ into the identity: $\tan(\theta + 25)=\cot(90 - (\theta + 25))$.

Step3: Simplify the argument of cotangent

Simplify $90 - (\theta + 25)$: $90-\theta - 25 = 65-\theta$. So, $\tan(\theta + 25)=\cot(65 - \theta)$.

Answer:

$\cot(65 - \theta)$