Use the cofunction identities to find an angle θ that makes the statement true.
-$\tan \theta = \cot \left( 30 ^ { \circ } + 5 \theta \right)$
A) $\theta = 75 ^ { \circ }$
B) $\theta = 10 ^ { \circ }$
C) $\theta = 16 ^ { \circ }$
D) $\theta = 6 ^ { \circ }$

Question

Quizplus · Accepted Answer

The cofunction identity for tangent and cotangent is $\tan \theta = \cot (90^\circ - \theta)$. Setting the given equation $\tan \theta = \cot (30^\circ + 5\theta)$ equal to each other and applying the cofunction identity, we get $\theta = 90^\circ - (30^\circ + 5\theta)$. Solving for $\theta$, we find $\theta = 10^\circ$.

Use the Cofunction Identities to Find an Angle θ That tan⁡θ=cot⁡(30∘+5θ)\tan \theta = \cot \left( 30 ^ { \circ } + 5 \theta \right)tanθ=cot(30∘+5θ)

Use the Cofunction Identities to Find an Angle θ That $\tan \theta = \cot \left( 30 ^ { \circ } + 5 \theta \right)$