Question

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

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

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

Proving trigonometry identity

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