MCQMathematics

MP Board · Class 10 · Mathematics · Introduction to TrigonometryIf $\tan 2A = \cot(A - 18^\circ)$, where $2A$ is an acute angle, then the value of $A$ is:

Step-by-Step Solution

We know that $\tan 2A = \cot(90^\circ - 2A)$. Given equation is $\tan 2A = \cot(A - 18^\circ)$. Equating the angles, we get $90^\circ - 2A = A - 18^\circ$. Rearranging terms: $90^\circ + 18^\circ = 2A + A$, which gives $3A = 108^\circ$. Therefore, $A = \frac{108^\circ}{3} = 36^\circ$.

Detailed Options Breakdown
Option : $18^\circ$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.

Option 1: $24^\circ$

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Introduction to Trigonometry.

Option 2: $36^\circ$ (Correct Answer)

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

Option 3: $45^\circ$

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.
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