Mathematics: Use basic identities to simplify the expression. cosecant of theta times cotangent of theta divided by secant of theta.

The correct answer would be the 3rd one because the number simplified equals that...

Use basic identities to simplify the expression.

Ответ:

pineapplequeen1912

04.01.2022

Mathematics

$cotg^{2} \theta$

Step-by-step explanation:

The given expression is:

$\frac{csc\theta (ctg\theta)}{sec\theta}$

But, we know that:

$csc\theta=\frac{1}{sin\theta}$

$ctg\theta = \frac{cos\theta}{sin\theta}$

$sec\theta=\frac{1}{cos\theta}$

Replacing all these basic identities in the given expression, we have:

$\frac{csc\theta (ctg\theta)}{sec\theta}\\\frac{\frac{1}{sin\theta}\frac{cos\theta}{sin\theta}}{\frac{1}{cos\theta}}\\\frac{cos^{2}\theta}{sin^{2} \theta }\\(\frac{cos\theta}{sin\theta})^{2}\\cotg^{2} \theta$

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Use basic identities to simplify the expression.

cosecant of theta times cotangent of theta divided by secant of theta.

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