Use the even-odd identities to evaluate the expression. cos ( − θ ) − cos θ \cos\left(-\theta\right)-\cos\theta cos ( − θ ) − cos θ

Here we're asked to use our even odd identities in order to evaluate the expression. And here our expression is the cosine of negative theta minus the cosine of theta. Now using my even odd identity here, I'm gonna replace this negative argument. Now the cosine of negative theta is simply the cosine of theta. So this ends up being the cosine of theta minus the cosine of theta. Now if I subtract that thing from itself I end up with 0 so the cosine of theta minus the cosine of theta is simply 0 and we're done here. The cosine of negative theta minus the cosine of theta is 0. Thanks for watching and I'll see you in the next one.

Use the even-odd identities to evaluate the expression. cos ⁡ ( − θ ) − cos ⁡ θ \cos\left(-\theta\right)-\cos\theta cos ( − θ ) − cos θ

− cos ⁡ θ -\cos\theta − cos θ

2 cos ⁡ θ 2\cos\theta 2 cos θ

− 2 cos ⁡ θ -2\cos\theta − 2 cos θ

6. Trigonometric Identities and More Equations

Introduction to Trigonometric Identities

Trigonometry

6. Trigonometric Identities and More Equations

Introduction to Trigonometric Identities

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Multiple Choice

Use the even-odd identities to evaluate the expression.
$\cos\left(-\theta\right)-\cos\theta$

$-\cos\theta$

$2\cos\theta$

$-2\cos\theta$

Verified step by step guidance

Understand the even-odd identities: In trigonometry, even functions satisfy f(-x) = f(x), and odd functions satisfy f(-x) = -f(x). The cosine function is an even function, meaning cos(-θ) = cos(θ).

Apply the even identity to the expression: Given cos(-θ) - cos(θ), use the identity cos(-θ) = cos(θ) to rewrite the expression as cos(θ) - cos(θ).

Simplify the expression: Since cos(θ) - cos(θ) results in 0, the expression simplifies to 0.

Consider the options provided: The correct answer is 0, which matches the simplified expression.

Reflect on the properties of trigonometric functions: Recognizing even and odd identities can simplify expressions and help solve problems efficiently.