Question

The reciprocal identities state that

$\mathit{c}\mathit{s}\mathit{c}\mathit{\theta }\mathbf{=}\frac{\mathbf{1}}{\mathbf{\square }}\mathit{s}\mathit{e}\mathit{c}\mathit{\theta }\mathbf{=}\frac{\mathbf{1}}{\mathbf{\square }}\mathit{c}\mathit{o}\mathit{t}\mathit{\theta }\mathbf{=}\frac{\mathbf{1}}{\mathbf{\square }}$

Short answer

The reciprocal identities are

$\begin{array}{l}\mathbf{c}\mathbf{s}\mathbf{c}\mathbf{\theta }\mathbf{=}\frac{\mathbf{1}}{\mathbf{s}\mathbf{i}\mathbf{n}\mathbf{\theta }}\\ \mathbf{s}\mathbf{e}\mathbf{c}\mathbf{\theta }\mathbf{=}\frac{\mathbf{1}}{\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{\theta }}\\ \mathbf{c}\mathbf{o}\mathbf{t}\mathbf{\theta }\mathbf{=}\frac{\mathbf{1}}{\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{\theta }}\end{array}$

Step-by-step solution

Step 1. Given information.

Given: Reciprocal identities of$\csc \theta ,\sec \theta$ and$\cot \theta$.
To find the reciprocal identities.
The cosecant angle is the reciprocal of sine.

Step 2. Value of csc θ.

that is,$\csc \theta =\frac{1}{\sin \theta }$

The secant angle is the reciprocal of cosine.

Step 3. Value of secθ.

that is,$\sec \theta =\frac{1}{\cos \theta }$
The cot angle is the reciprocal of tangent.

Step 4. Value of cotθ.

The cot angle is the reciprocal of tangent that is,$\cot \theta =\frac{1}{\tan \theta }$