Chapter 7: Q. 11 (page 505)

Establish the identity
$\frac{c s c θ + c o t θ}{s e c θ + \tan θ} = \frac{s e c θ - \tan θ}{c s c θ - c o t θ}$

Short Answer

Expert verified

Rationalizing the numerator and denominator by multiply numerator and denominator by

$c s c θ - c o t θ a n d s e c θ - \tan θ w e g e t \frac{c s c θ + c o t θ}{s e c θ + \tan θ} = \frac{s e c θ - \tan θ}{c s c θ - c o t θ}$

Step by step solution

Step 1. Given information

\frac{c s c θ + c o t θ}{s e c θ + \tan θ} = \frac{s e c θ - \tan θ}{c s c θ - c o t θ}

Step 2. Rationalizing the numerator and denominator

$W e h a v e g i v e n, \frac{c s c θ + c o t θ}{s e c θ + \tan θ} = \frac{s e c θ - \tan θ}{c s c θ - c o t θ} T a k e L H S \frac{c s c θ + c o t θ}{s e c θ + \tan θ}$

Rationalizing the numerator and denominator by multiply numerator and denominator by $c s c θ - c o t θ a n d s e c θ - \tan θ$

$(\frac{c s c θ + c o t θ}{s e c θ + \tan θ}) (\frac{c s c θ - c o t θ}{c s c θ - c o t θ}) (\frac{s e c θ - \tan θ}{s e c θ - \tan θ}) = \frac{(c s c^{2} θ - c o t^{2} θ) (s e c θ - \tan θ)}{(s e c^{2} θ - \tan^{2} θ) (c s c θ - c o t θ)} a s c s c^{2} θ - c o t^{2} θ = 1 s e c^{2} θ - \tan^{2} θ = 1 = \frac{s e c θ - \tan θ}{c s c θ - c o t θ}$

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Establish the identity
$\frac{c s c θ + c o t θ}{s e c θ + \tan θ} = \frac{s e c θ - \tan θ}{c s c θ - c o t θ}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Rationalizing the numerator and denominator

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Establish the identitycscθ+cotθsecθ+tanθ=secθ-tanθcscθ-cotθ

Short Answer

Step by step solution

Step 1. Given information

Step 2. Rationalizing the numerator and denominator

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Pure Maths

Applied Mathematics

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Establish the identity
$\frac{c s c θ + c o t θ}{s e c θ + \tan θ} = \frac{s e c θ - \tan θ}{c s c θ - c o t θ}$