Prove that (sin4θ – cos4θ +1) cosec2θ = 2

To prove that \((\sin 4\theta - \cos 4\theta + 1) \csc^2\theta = 2\), let's start by simplifying the left-hand side.

### Step 1: Express \(\sin 4\theta - \cos 4\theta\) using the identity
We can use the identity for the difference of squares:
\[
\sin^2 4\theta - \cos^2 4\theta = (\sin 4\theta - \cos 4\theta)(\sin 4\theta + \cos 4\theta)
\]
However, here we have \(\sin 4\theta - \cos 4\theta\), so we

Learn how to prove the trigonometric identity (sin4θ – cos4θ +1) cosec2θ = 2 step-by-step. This problem involves using trigonometric identities and is suitable for advanced high school students.

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