NCERT Class 11 Mathematics — The value of $\sin 75^{\circ}

NCERT · Class 11 · Mathematics · Trigonometric FunctionsThe value of $\sin 75^{\circ}$ is:

Step-by-Step Solution

We can write $\sin(75^{\circ}) = \sin(45^{\circ} + 30^{\circ})$. Using the formula $\sin(A + B) = \sin A \cos B + \cos A \sin B$, we get $\sin(45^{\circ})\cos(30^{\circ}) + \cos(45^{\circ})\sin(30^{\circ}) = \left(\frac{1}{\sqrt{2}}\right)\left(\frac{\sqrt{3}}{2}\right) + \left(\frac{1}{\sqrt{2}}\right)\left(\frac{1}{2}\right) = \frac{\sqrt{3} + 1}{2\sqrt{2}} = \frac{\sqrt{6} + \sqrt{2}}{4}$.

Detailed Options Breakdown

Option : \frac{\sqrt{6} - \sqrt{2}}{4}

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Trigonometric Functions.

Option 1: \frac{\sqrt{3} + 1}{2}

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Trigonometric Functions.

Option 2: \frac{\sqrt{6} + \sqrt{2}}{4} (Correct Answer)

Correct choice. Refer to the step-by-step verified solution guidelines above for details.

Option 3: \frac{\sqrt{3} - 1}{2\sqrt{2}}

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Trigonometric Functions.

💡 Study Guide: This question tests core syllabus concepts from Trigonometric Functions. For formulas, key summaries, and mock exam reference guides, read the full Trigonometric Functions Revision Notes.

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Verified by Academic Committee