Trigonometry
Solutions of Trigonometric Equations
MJAT Test Series
Grade 12
Question:
Consider the following lists: List-I List-II (I) $\{x \in [-2\pi/3, 2\pi/3] : \cos x + \sin x = 1\}$ (P) has two elements (II) $\{x \in [-5\pi/18, 5\pi/18] : \sqrt{3} \tan 3x = 1\}$ (Q) has three elements (III) $\{x \in [-6\pi/5, 6\pi/5] : 2 \cos (2x) = \sqrt{3}\}$ (R) has four elements (IV) $\{x \in [-7\pi/4, 7\pi/4] : \sin x - \cos x = 1\}$ (S) has five elements (T) has six elements. The correct option is:
A) (I) \rightarrow (P); (II) \rightarrow (S); (III) \rightarrow (P); (IV) \rightarrow (S)
B) (I) \rightarrow (P); (II) \rightarrow (P); (III) \rightarrow (T); (IV) \rightarrow (R)
C) (I) \rightarrow (Q); (II) \rightarrow (P); (III) \rightarrow (T); (IV) \rightarrow (S)
D) (I) \rightarrow (Q); (II) \rightarrow (S); (III) \rightarrow (P); (IV) \rightarrow (R)
Step-by-Step Solution
Key Concept: Use standard formulaic analysis.
Direct stepwise solution placeholder.
Correct Answer: B