The trigonometric equation sin ^-1 x=2 sin ^-1 a has a solution for
JEE Main 2003 — Mathematics Trigonometry
2003mcqmedium
The trigonometric equation sin−1x=2sin−1 a has a solution for
Official previous-year question
Held on 30 Apr 2003 · Verified 6 Jul 2026.
Options
A
∣a∣≥21
B
21<∣a∣<21
C
all real values of a
D
∣a∣<21
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Solution
sin−1x=2sin−1a−2π≤sin−1x≤2π;∴−2π≤2sin−1a≤2π−4π≤sin−1a≤4π or 2−1≤a≤21∴∣a∣≤21( As 21>21 ). Out of given four option no one is absolutely correct but (c) could be taken into consideration. →∣a∣≤21 is correct, if a<21 is taken as correct then it domain satisfy for a=31 but equation is satisfied. 21>31>21
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