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ID:
Class: 11
Subject: Math
Topic: Trigonometric Functions
Type: Short
Question:
Prove that: \[ \sin(n+1)x \cdot \sin(n+2)x + \cos(n+1)x \cdot \cos(n+2)x = \cos x \]
Official Solution
Explanation:
\begin{align*}
\text{LHS} &= \sin(n+1)x \cdot \sin(n+2)x + \cos(n+1)x \cdot \cos(n+2)x \\
&= \cos\left[ (n+1)x - (n+2)x \right] \\
&= \cos(-x) = \cos x = \text{RHS} \qquad \textbf{Hence proved.}
\end{align*}
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