Chapter 7: Q. 69 (page 475)

In problems 19-98, establish each identity.
$\frac{\sec (θ) - \csc (θ)}{\sec (θ) \csc (θ)} = \sin (θ) - \cos (θ)$

Short Answer

Expert verified

We have proved the identity $\frac{\sec (θ) - \csc (θ)}{\sec (θ) \csc (θ)} = \sin (θ) - \cos (θ)$ .

Step by step solution

Step 1. Given information.

We have:

$\frac{\sec (θ) - \csc (θ)}{\sec (θ) \csc (θ)} = \sin (θ) - \cos (θ)$

Step 2. Establish the identity.

Take the left hand side:

$\frac{\sec (θ) - \csc (θ)}{\sec (θ) \csc (θ)} = \frac{\frac{1}{\cos (θ)} - \frac{1}{\sin (θ)}}{\frac{1}{\cos (θ)} \times \frac{1}{\sin (θ)}} = \frac{\frac{\sin (θ) - \cos (θ)}{\cos (θ) \sin (θ)}}{\frac{1}{\cos (θ) \sin (θ)}} = \frac{\sin (θ) - \cos (θ)}{\cos (θ) \sin (θ)} \times \frac{\cos (θ) \sin (θ)}{1} = \sin (θ) - \cos (θ)$

Hence, proved.

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In problems 19-98, establish each identity.
$\frac{\sec (θ) - \csc (θ)}{\sec (θ) \csc (θ)} = \sin (θ) - \cos (θ)$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Establish the identity.

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In problems 19-98, establish each identity.secθ-cscθsecθcscθ=sinθ-cosθ

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Establish the identity.

One App. One Place for Learning.

Most popular questions from this chapter

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Probability and Statistics

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Study anywhere. Anytime. Across all devices.

In problems 19-98, establish each identity.
$\frac{\sec (θ) - \csc (θ)}{\sec (θ) \csc (θ)} = \sin (θ) - \cos (θ)$