θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value.
-$\tan 55 ^ { \circ } \cot 55 ^ { \circ }$
A) 1
B) 0
C) 55
D) $- 1$

Question

Quizplus · Accepted Answer

The product of $\tan \theta$ and $\cot \theta$ is always 1, because $\tan \theta = \frac{\sin \theta}{\cos \theta}$ and $\cot \theta = \frac{\cos \theta}{\sin \theta}$, so their product is $\frac{\sin \theta}{\cos \theta} \cdot \frac{\cos \theta}{\sin \theta} = 1$.

θ Is an Acute Angle and Sin θ and Cos tan⁡55∘cot⁡55∘\tan 55 ^ { \circ } \cot 55 ^ { \circ }tan55∘cot55∘

θ Is an Acute Angle and Sin θ and Cos $\tan 55 ^ { \circ } \cot 55 ^ { \circ }$