Use the cofunction identities to find an angle θ that makes the statement true.
-$\cot \left( 2 \theta - 20 ^ { \circ } \right) = \tan \left( \theta - 10 ^ { \circ } \right)$
A) $\theta = \frac { 17 ^ { \circ } } { 7 }$
B) $\theta = 10 ^ { \circ }$
C) $\theta = \frac { 83 ^ { \circ } } { 7 }$
D) $\theta = 40 ^ { \circ }$

Question

Quizplus · Accepted Answer

The cofunction identity for cotangent and tangent is $\cot(x) = \tan(90^\circ - x)$. Setting $2\theta - 20^\circ = 90^\circ - (\theta - 10^\circ)$ and solving for $\theta$ gives $\theta = 40^\circ$.

Use the Cofunction Identities to Find an Angle θ That cot⁡(2θ−20∘)=tan⁡(θ−10∘)\cot \left( 2 \theta - 20 ^ { \circ } \right) = \tan \left( \theta - 10 ^ { \circ } \right)cot(2θ−20∘)=tan(θ−10∘)

Use the Cofunction Identities to Find an Angle θ That $\cot \left( 2 \theta - 20 ^ { \circ } \right) = \tan \left( \theta - 10 ^ { \circ } \right)$