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

Question

Quizplus · Accepted Answer

The cotangent and tangent functions are cofunctions of each other, meaning $\cot(x) = \tan(90^\circ - x)$. Therefore, if $\cot(2\theta - 20^\circ) = \tan(\theta - 10^\circ)$, 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\thetaθ That Makes the Statement True

Use the Cofunction Identities to Find an Angle $\theta$ That Makes the Statement True