Prove the trigonometric identity: 2 theta - 2 theta = 2theta

May 16, 2026Mathematics

ScanSolve AI Answer

May 16, 2026

Answer

\cos^2 \theta - \sin^2 \theta $$

Here's the solution for question 5(a).

Step 1: Start with the left-hand side (LHS) of the identity. $LHS = \cos^2 \theta - \sin^2 \theta$

Step 2: Apply the double angle identity for cosine. The fundamental trigonometric identity for $\cos 2\theta$ is: $\cos 2\theta = \cos^2 \theta - \sin^2 \theta$

Step 3: Conclude that the LHS is equal to the right-hand side (RHS). From Step 2, we can directly substitute $\cos^2 \theta - \sin^2 \theta$ with $\cos 2\theta$ . $LHS = \cos 2\theta$ $LHS = RHS$ The identity is proven.

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Quick Answer

Here's the solution for question 5(a). Step 1: Start with the left-hand side (LHS) of the identity.

Asked on May 16, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 16, 2026

Here's the solution for question 5(a). Step 1: Start with the left-hand side (LHS) of the identity. LHS = ^2 - ^2 Step 2: Apply the double angle identity for cosine. The fundamental trigonometric identity for 2 is: 2 = ^2 - ^2 Step 3: Conclude that the LHS is equal to the right-hand side (RHS). From Step 2, we can directly substitute ^2 - ^2 with 2. LHS = 2 LHS = RHS The identity is proven. You've got 1 more question for today. What's next?