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2022-04-02 Answered

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user_27qwe

Answered 2022-04-21 Author has 208 answers

$\tan^{2} (α) - \sin^{2} (α) = \tan^{2} (α) \sin^{2} (α)$ Start on the left side.

$\tan^{2} (α) - \sin^{2} (α)$

Convert to sines and cosines.

Write $\tan (α)$ in sines and cosines using the quotient identity.

${(\frac{\sin (α)}{\cos (α)})}^{2} - \sin^{2} (α)$

Apply the product rule to $\frac{\sin (α)}{\cos (α)}$ .

$\frac{\sin^{2} (α)}{\cos^{2} (α)} - \sin^{2} (α)$

Write $- \sin^{2} (α)$ as a fraction with denominator $1$ .

$\frac{\sin^{2} (α)}{\cos^{2} (α)} + \frac{- \sin^{2} (α)}{1}$

Add fractions.

To write $\frac{- \sin^{2} (α)}{1}$ as a fraction with a common denominator, multiply by $\frac{\cos^{2} (α)}{\cos^{2} (α)}$ .

$\frac{\sin^{2} (α)}{\cos^{2} (α)} + \frac{- \sin^{2} (α)}{1} \cdot \frac{\cos^{2} (α)}{\cos^{2} (α)}$

Multiply $\frac{- \sin^{2} (α)}{1}$ by $\frac{\cos^{2} (α)}{\cos^{2} (α)}$ .

$\frac{\sin^{2} (α)}{\cos^{2} (α)} + \frac{- \sin^{2} (α) \cos^{2} (α)}{\cos^{2} (α)}$

Combine the numerators over the common denominator.

$\frac{\sin^{2} (α) - \sin^{2} (α) \cos^{2} (α)}{\cos^{2} (α)}$

Apply Pythagorean identity.

Multiply by $1$ .

$\frac{\sin^{2} (α) \cdot 1 - \sin^{2} (α) \cos^{2} (α)}{\cos^{2} (α)}$

Factor $\sin^{2} (α)$ out of $- \sin^{2} (α) \cos^{2} (α)$ .

$\frac{\sin^{2} (α) \cdot 1 + \sin^{2} (α) (- \cos^{2} (α))}{\cos^{2} (α)}$

Factor $\sin^{2} (α)$ out of $\sin^{2} (α) \cdot 1 + \sin^{2} (α) (- \cos^{2} (α))$ .

$\frac{\sin^{2} (α) \cdot (1 - \cos^{2} (α))}{\cos^{2} (α)}$

Apply pythagorean identity.

$\frac{\sin^{2} (α) \cdot \sin^{2} (α)}{\cos^{2} (α)}$

Multiply ${\sin (α)}^{2}$ by ${\sin (α)}^{2}$ by adding the exponents.

$\frac{\sin^{4} (α)}{\cos^{2} (α)}$

Rewrite $\frac{\sin^{4} (α)}{\cos^{2} (α)}$ as $\tan^{2} (α) \sin^{2} (α)$ .

$\tan^{2} (α) \sin^{2} (α)$

Because the two sides have been shown to be equivalent, the equation is an identity.

$\tan^{2} (α) - \sin^{2} (α) = \tan^{2} (α) \sin^{2} (α)$ is an identity

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Site	Period	Size (in ha.)	# Ceremonial Structures	Distance to Coast (in km)	% Marine Resources(before)	% Marine Resources(after)
1	1	3.40	5.00	3.20	61.00	58.00
2	1	9.80	7.00	1.20	56.00	55.00
3	1	4.20	6.00	3.30	54.00	52.00
1	1	1.20	2.00	7.30	31.00	29.00
2	1	3.30	6.00	4.40	61.00	60.00
3	1	2.50	4.00	5.30	45.00	45.00
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1	1	2.20	2.00	6.70	32.00	30.00
2	1	2.80	3.00	5.20	61.00	60.00
3	1	2.90	4.00	4.20	67.00	66.00
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3	2	9.40	6.00	7.50	32.00	30.00
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3	2	2.20	2.00	8.50	26.00	25.00
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1	2	4.10	3.00	9.10	12.00	11.00
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