Prove the Identity: ( theta + 2theta * theta)/( theta) = theta

May 4, 2026Mathematics

ScanSolve AI Answer

May 4, 2026

Answer

\tan \theta$

Hey MaMofokeng🌏❤️ — ready when you are.

Let's prove the first identity.

1) Prove the Identity: $\frac{\cos \theta + \sin 2\theta \cdot \sec \theta}{\csc \theta} = \tan \theta$

Step 1: Rewrite the left-hand side (LHS) in terms of $\sin \theta$ and $\cos \theta$ . We use the identities: $\sin 2\theta = 2 \sin \theta \cos \theta$ $\sec \theta = \frac{1}{\cos \theta}$ $\csc \theta = \frac{1}{\sin \theta}$

Substitute these into the LHS:

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Hey MaMofokeng🌏❤️ — ready when you are. Let's prove the first identity.

Asked on May 4, 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 4, 2026

Hey MaMofokeng🌏❤️ — ready when you are. Let's prove the first identity. 1) Prove the Identity: ( + 2 · )/( ) = Step 1: Rewrite the left-hand side (LHS) in terms of and . We use the identities: 2 = 2 = (1)/( ) = (1)/( ) Substitute these into the LHS: LHS =