Use the cofunction identities to find an angle θ that makes the statement true.
-$\tan \left( 2 \theta - 140 ^ { \circ } \right) = \cot \left( \theta + 5 ^ { \circ } \right)$
A) $\theta = 75 ^ { \circ }$
B) $\theta = 10 ^ { \circ }$
C) $\theta = 6 ^ { \circ }$
D) $\theta = 16 ^ { \circ }$

Question

Quizplus · Accepted Answer

The cofunction identity for tangent and cotangent is $\tan(\alpha) = \cot(90^\circ - \alpha)$. Setting the given equation $\tan(2\theta - 140^\circ) = \cot(\theta + 5^\circ)$ equal, we can use the identity to find that $2\theta - 140^\circ = 90^\circ - (\theta + 5^\circ)$. Solving for $\theta$ gives $\theta = 75^\circ$.

Use the Cofunction Identities to Find an Angle θ That tan⁡(2θ−140∘)=cot⁡(θ+5∘)\tan \left( 2 \theta - 140 ^ { \circ } \right) = \cot \left( \theta + 5 ^ { \circ } \right)tan(2θ−140∘)=cot(θ+5∘)

Use the Cofunction Identities to Find an Angle θ That $\tan \left( 2 \theta - 140 ^ { \circ } \right) = \cot \left( \theta + 5 ^ { \circ } \right)$