Verify using proofs **Trigonometric Identity Proof**The image presents a trigonometric identity that needs to be proven:\[ \cos^2 \theta = \frac{1 + \cos 2\theta}{2} \]**Explanation:**This identity relates the square of the cosine of an angle (\(\theta\)) to the cosine of twice that angle (\(2\theta\)). It is a commonly used identity in trigonometry known as the "Power-Reduction Formulas." These formulas are useful for simplifying expressions involving trigonometric functions to make integration or equation-solving more manageable.**Proof Overview:**To prove this identity, we can start by using the double-angle formula for cosine:\[ \cos 2\theta = 2\cos^2 \theta - 1 \]Rearrange the formula to express \(\cos^2 \theta\):\[ 2\cos^2 \theta = 1 + \cos 2\theta \]Now, divide both sides by 2:\[ \cos^2 \theta = \frac{1 + \cos 2\theta}{2} \]This completes the proof, verifying the identity as shown in the equation.

Name: Verify using proofs **Trigonometric Identity Proof**The image presents
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: Verify using proofs **Trigonometric Identity Proof**The image presents a trigonometric identity that needs to be proven:\[ \cos^2 \theta = \frac{1 + \cos 2\theta}{2} \]**Explanation:**This identity relates the square of the cosine of an angle (\(\the