Chapter 7: Q. 13 (page 505)

Establish the identity
$\tan θ + c o t θ = 2 c s c (2 θ)$

Short Answer

Expert verified

By converting tan $θ$ and cot $θ$ into sin $θ$ and cos $θ$

we get the tan $θ$ + cot $θ$ =2csc(2 $θ$ )

Step by step solution

Step 1. Given information

$\tan θ + c o t θ = 2 c s c (2 θ)$

Step 2. Calculations

$\tan θ + c o t θ = 2 c s c (2 θ) T a k e L H S, \tan θ + c o t θ \frac{\sin θ}{\cos θ} + \frac{\cos θ}{\sin θ} = \frac{\sin^{2} θ + \cos^{2} θ}{\cos θ \sin θ} \tan θ = \frac{\sin θ}{\cos θ} c o t θ = \frac{\cos θ}{\sin θ} = \frac{1}{\cos θ \sin θ} = \frac{2}{2 \cos θ \sin θ} = \frac{2}{\sin 2 θ} 2 \cos θ \sin θ = \sin 2 θ = 2 c s c (2 θ)$

Hence LHS=RHS

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Establish the identity
$\tan θ + c o t θ = 2 c s c (2 θ)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculations

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Establish the identity tanθ+cotθ=2csc(2θ)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculations

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Establish the identity
$\tan θ + c o t θ = 2 c s c (2 θ)$