Home › Bihar Board Class 12 (Commerce) › Mathematics › Inverse Trigonometric Functions › sin⁻¹(2x√(1 - x²)) = 2 sin⁻¹x is valid for which…
sin⁻¹(2x√(1 - x²)) = 2 sin⁻¹x is valid for which x?
A[-1/√2, 0]
B[0, 1/√2]
C[-1, 1/√2]
D[-1/√2, 1/√2]
Answer & Solution
Correct answer: D. [-1/√2, 1/√2]
Put x = sin θ; then 2θ must lie in [-π/2, π/2], so θ is within ±π/4 and |x| ≤ 1/√2.
Related questions
Principal cot⁻¹ evaluated at 0 equalsCotangent restricted to which interval is bijective onto R?Inverse trigonometric functions are important in calculus because theyFor an invertible f, what does (f⁻¹ o f)(x) equal?The inverse of f exists only if f isThales is credited with finding the height of a pyramid using what?Which country is credited with starting the study of trigonometry?Who suggested the symbols sin⁻¹x and cos⁻¹x for arc sin x and arc cos x?