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 going to 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 zero. So the cosine of theta minus the cosine of theta is simply zero and we're done here. The cosine of negative theta minus the cosine of theta is zero. 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

12. Trigonometric Functions

Trigonometric Identities

Business Calculus

12. Trigonometric Functions

Trigonometric Identities

Struggling with Business Calculus?

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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

Step 1: Recall the even-odd identities for trigonometric functions. The cosine function is an even function, meaning that cos(−θ) = cos(θ).

Step 2: Substitute the even-odd identity into the given expression. Replace cos(−θ) with cos(θ) in the expression cos(−θ) − cos(θ).

Step 3: Simplify the expression. After substitution, the expression becomes cos(θ) − cos(θ).

Step 4: Perform the subtraction. Since cos(θ) − cos(θ) equals 0, the simplified result of the expression is 0.

Step 5: Verify the result using the properties of trigonometric functions and confirm that the correct answer is indeed 0.

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

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Trigonometric Identities practice set

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