NCERT · Class 10 · Mathematics · Introduction to TrigonometryWhat is the value of $\frac{1 - \tan^2 45^\circ}{1 + \tan^2 45^\circ}$?
Step-by-Step Solution
We know that $\tan 45^\circ = 1$. \nSubstituting this value into the given expression: $$\frac{1 - \tan^2 45^\circ}{1 + \tan^2 45^\circ} = \frac{1 - (1)^2}{1 + (1)^2} = \frac{1 - 1}{1 + 1} = \frac{0}{2} = 0$$ \nHence, the correct option is (D).
Detailed Options Breakdown
Option : $\tan 90^\circ$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.
Option 1: $1$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.
Option 2: $\sin 45^\circ$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.
Option 3: $0$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
💡 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.