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storchak [24]
2 years ago
5

(cot theta + cosec theta)/(cosec theta (1 + (cot theta/ cosec theta)).

Mathematics
2 answers:
bekas [8.4K]2 years ago
6 0

Answer:

Below:

Step-by-step explanation:

Your Answer is in the picture below:

Hope it helps...

It's Miss-Muska

Margarita [4]2 years ago
4 0

The given expression \dfrac{\frac{cos \theta}{sin \theta}  + \frac{1}{sin\theta} }{\frac{1}{sin \theta} (1+cos \theta)} =1 is true

<h3>Proving trigonometry identity</h3>

Given the expression

\frac{cot \theta + cosec \theta}{cosec \theta(1+\frac{cot \theta}{cosec \theta} )} =1

Note that:

  • cotθ = cosθ/sinθ
  • cosecθ = 1/sinθ

Substituting the given parameters into the formula;

\frac{\frac{cos \theta}{sin \theta}  + \frac{1}{sin\theta} }{\frac{1}{sin \theta} (1+cos \theta)} =1

Find the LCM of both the numerator and denominator

= \dfrac{\frac{cos \theta + 1}{sin \theta} }{(\frac{1+cos \theta}{sin \theta} )}\\

Divide the result to have:

= \frac{1+cos \theta}{sin \theta} \times \frac{sin \theta}{1+cos \theta}\\ = \frac{1}{1}\\ = 1 (Proved)

Learn more on proofs of trigonometry identity here: brainly.com/question/7331447

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