Use the fundamental identities to simplify the expression.
-$\cot \left( 2 \theta - 20 ^ { \circ } \right) = \tan \left( \theta - 10 ^ { \circ } \right)$
A) $\theta = 10 ^ { \circ }$
B) $\theta = 40 ^ { \circ }$
C) $\theta = \frac { 17 ^ { \circ } } { 7 }$
D) $\theta = \frac { 83 ^ { \circ } } { 7 }$

Question

Quizplus · Accepted Answer

Using the identity $\cot(x) = \tan(90^\circ - x)$, we have $\cot(2\theta - 20^\circ) = \tan(90^\circ - (2\theta - 20^\circ)) = \tan(110^\circ - 2\theta)$. Setting $\tan(110^\circ - 2\theta) = \tan(\theta - 10^\circ)$, we solve for $\theta$ and find $\theta = 40^\circ$.

Use the Fundamental Identities to Simplify the Expression 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 Fundamental Identities to Simplify the Expression $\cot \left( 2 \theta - 20 ^ { \circ } \right) = \tan \left( \theta - 10 ^ { \circ } \right)$