### Home > PC3 > Chapter Ch8 > Lesson 8.3.3 > Problem8-115

8-115.

Simplify each the following trigonometric expressions.

1. $\cos\left(A\right)\cot\left(A\right) + \sin\left(A\right)$

1. Rewrite everything in terms of sine and cosine.
2. Get a common denominator.
3. Use the Fundamental Pythagorean Identity.
4. Simplify.

2. $\sin^2\left(θ\right)+\tan^2\left(θ\right)-\cot^2\left(θ\right)+\cos^2\left(θ\right)-\sec^2\left(θ\right)+\csc^2\left(θ\right)$

Use the Pythagorean Identities.
Change their forms to get $1$s.

$\cos^{2}\left(θ\right) + \sin^{2}\left(θ\right) = 1$
$1 + \tan^{2}\left(θ\right) = \sec^{2}\left(θ\right)$
$1 + \cot^{2}\left(θ\right) = \csc^{2}\left(θ\right)$
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