The trigonometric equation ^-1 x = 2 ^-1 a , has a solution for: - Mathematics MCQ AIEEE-CBSE-ENG-03 2026 | ExamTest.live

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The trigonometric equation sin^{- 1} x = 2 sin^{- 1} a, has a solution for:

Solution & Step-by-step Explanation

The range of sin^{- 1} x is [- π /2, π /2] .For the equation to have a solution: - \frac{π}{2} \leq 2 sin^{- 1} a \leq \frac{π}{2} - \frac{π}{4} \leq sin^{- 1} a \leq \frac{π}{4} Taking sine on all sides: sin (- π /4) \leq a \leq sin (π /4) - \frac{1}{2} \leq a \leq \frac{1}{2} This is equivalent to ∣ a ∣ \leq \frac{1}{2} .

Try it yourself before checking the explanation above.

The trigonometric equation sin^{- 1} x = 2 sin^{- 1} a, has a solution for:

\frac{1}{2} < ∣ a ∣ < \frac{1}{2}

all real values of a

∣ a ∣ < \frac{1}{2}

∣ a ∣ \leq \frac{1}{2}

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