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Lelu [443]
3 years ago
9

Use basic identities to simplify the expression.

Mathematics
2 answers:
scoundrel [369]3 years ago
8 0
(csc*cot)/ sec

change everything into sin or cos and simplify

((1/sin)*(cos/sin))/ (1/cos)

=(cos/sin^2)/ (1/cos)

=(cos/sin^2) * (cos/1)

=cos^2/ sin^2
stiks02 [169]3 years ago
3 0

Answer:

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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