CBSE · Class 10 · Mathematics · Introduction to TrigonometryWhat is the simplified form of $(\1 - \cos \theta)(1 + \cos \theta)(\1 + \cot^2 \theta)$?
Step-by-Step Solution
Using algebraic identity $(1 - \cos \theta)(1 + \cos \theta) = 1 - \cos^2 \theta = \sin^2 \theta$. Also, we know $1 + \cot^2 \theta = \csc^2 \theta = \frac{1}{\sin^2 \theta}$. Multiplying them together: $\sin^2 \theta \times \frac{1}{\sin^2 \theta} = 1$.
Detailed Options Breakdown
Option : 0
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.
Option 1: 1 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: -1
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.
Option 3: sin $\theta$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.
💡 Study Guide: This question tests core syllabus concepts from Introduction to Trigonometry. For formulas, key summaries, and mock exam reference guides, read the full Introduction to Trigonometry Revision Notes.