UP TGT Mathematics Trigonometry Test Series - Part 1
The number of real roots of the equation e^{sin x} - e^{-sin x} - 4 = 0 is:
Type: MCQ • Marks: 1
The number of real roots of the equation e^{sin x} - e^{-sin x} - 4 = 0 is:
Options
A. 1
B. 2
C. Infinite
D. 0
Explanation
Let y = e^{sin x}. Since -1 ≤ sin x ≤ 1, 1/e ≤ y ≤ e. Equation becomes y - 1/y - 4 = 0 => y² - 4y - 1 = 0 => y = 2 ± √5. Max value of y is e ≈ 2.718, but 2 + √5 ≈ 4.236 > e, and 2 - √5 < 0. No solution exists. Number of real roots = 0.
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