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Question
If α ≤ 2 sin–1x + cos–1x ≤ β, then ______.
Options
α = `(-pi)/2`, β = `pi/2`
α = β = π
α = `(-pi)/2`, β = `(3pi)/2`
α = 0, β = 2π
Solution
If α ≤ 2 sin–1x + cos–1x ≤ β, then α = β = π.
Explanation:
We have `(-pi)/2 ≤ sin^-1x ≤ pi/2`
⇒ `(-pi)/2 + pi/2 ≤ sin^-1x + pi/2 ≤ pi/2 + pi/2`
⇒ 0 ≤ sin–1x + (sin–1x + cos–1x) ≤ π
⇒ 0 ≤ 2sin–1x + cos–1x ≤ π
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