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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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A + c = 824                             represents number of tickets to sell
20a + 12c = 13,344                represents cost of each type of ticket

multiply equation 1 by -12 to cancel the variable 'c' and solve for 'a'

-12(a + c = 824)

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-----------------------------
    8a          = 3456           divide both sides by 8
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To find children's tickets substitute adult numbers back into equation 1.
a + c = 824
432 + c = 824
subtract 432 from both sides
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We have been given that the take home pay is $1500 and 22% is withheld as taxes.

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