CPM Homework Help : PC Problem 4-112

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4-112.

Verify the following trigonometric identities. Intermediate steps may involve complex fractions.

$\operatorname{cot}^2 x(\operatorname{sec}^2 x − 1) = 1$
Hint (a):
Substitute a Pythagorean Identity for $\operatorname{sec}^2x$ .

$\operatorname{sin}^2 α − \operatorname{cos}^2 α = 1 − 2 \operatorname{cos}^2 α$
Hint (b):
Substitute the Fundamental Pythagorean Identity into the left side of the equation for $\operatorname{sin}^2α$ .

$\operatorname{tan}^2 β + 6 = \operatorname{sec}^2 β + 5$
Hint (c):
Substitute a Pythagorean Identity for $\operatorname{sec}^2x$ .

$\text{cos }y + \text{sin }y · \text{tan }y = \text{sec }y$
Hint (d):
Rewrite $\text{tan }y$ as $\text{sin }y$ / $\text{cos }y$ .
Get common denominators and simplify.

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