Bihar Board Class 12 (Science) Inverse Trigonometric Functions — practice questions
60 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice Bihar Board Class 12 (Science) Inverse Trigonometric Functions in the app →The domain of the function $f(x) = in^{-1}(x)$ isThe range of $\cos^{-1}(x)$ isFor every $x \in [-1, 1]$, the value of $ in^{-1}(x) + \cos^{-1}(x)$ isThe principal value of $\tan^{-1}(1)$ is$\tan^{-1}\left(\tfrac{1}{2}\right) + \tan^{-1}\left(\tfrac{1}{3}\right)$ equals$\cot^{-1}\left(-\tfrac{1}{ qrt{3}}\right) = $$ in^{-1}\left( in\tfrac{2\pi}{3}\right)$ equals$\cos^{-1}\left(\cos\tfrac{7\pi}{6}\right)$ equals$\tan^{-1}(1) + \tan^{-1}(2) + \tan^{-1}(3) = $$\displaystyle um_{n=1}^{\infty} \tan^{-1}\left(\frac{1}{n^2 + n + 1}\right)$ equalsFor $x = -2$, the value of $\tan^{-1}\left(\dfrac{2x}{1-x^2}\right)$ equalsAll real $x$ satisfying $ in^{-1}(x) + in^{-1}(1-x) = \cos^{-1}(x)$ areThe value of $\cos^{-1}(-1)$ is:The value of $ in(\tan^{-1}(3/4))$ is:Taking the principal branch, arcsin of one half is the angleWhich angle in [0, π] has cosine √3/2?If y = tan⁻¹(1) on its principal branch, y isFor the input -1/2, the principal branch of sin⁻¹ outputsEvaluating arccos(-0.5) on the principal branch givesWhich angle in (-π/2, π/2) has tangent equal to -√3?The angle in [-π/2, π/2], not 0, with cosecant 2 isDetermine sec⁻¹(2/√3) using the principal value branch.Applied to √3, principal cot⁻¹ returns, in radians,Give the principal angle whose cosine is -1/√2.On the principal branch, cosec⁻¹ returns what for input -√2?For the input -1/√3, principal cot⁻¹ gives which angle?An angle in [0, π] has secant -2. That angle isCompute tan⁻¹(√3) minus sec⁻¹(-2) using principal values.Evaluate tan⁻¹(1) + cos⁻¹(-1/2) + sin⁻¹(-1/2).Add cos⁻¹(1/2) to twice sin⁻¹(1/2); the total isIf sin⁻¹x = y, then y must satisfyCosine is made bijective on which interval to define cos⁻¹?On its principal branch, tan⁻¹ takes values in which set?Which line states the principal branch of cot⁻¹?The function sec⁻¹ accepts inputs from which set?Remove one point from [0, π] to define principal sec⁻¹. Which?For principal cosec⁻¹, [-π/2, π/2] must lose which point?Which function has domain R and range (0, π)?Why must the domain of sine be restricted before its inverse is defined?The function sin⁻¹ reverses which relation between x and y?The expression (sin x)⁻¹ is the same as which function?The curve y = sin⁻¹x is the reflection of y = sin x in which line?If no branch of an inverse trigonometric function is mentioned, which branch is meant?Which value does cos⁻¹(cos(7π/6)) take?Simplify tan⁻¹(tan 3π/4) on the principal branch.What does cos⁻¹(cos(-π/3)) reduce to?Find cos⁻¹(cos 2π) as a principal value.If sin⁻¹x = π/5, what is cos⁻¹x for the same x?The value of sec⁻¹(2) equals which of the following?cosec⁻¹ at -2, on the principal branch, equalsPrincipal arcsine of -√3/2 equals which angle?tan⁻¹(1/2) + tan⁻¹(1/3) simplifies toDoubling tan⁻¹(1/√3) gives3 sin⁻¹x = sin⁻¹(3x - 4x³) holds for x insin⁻¹(2x√(1 - x²)) = 2 sin⁻¹x is valid for which x?Express cot⁻¹[1/√(x² - 1)], x > 1, in simplest form.What is tan(cos⁻¹(4/5))?Add sin⁻¹(1) and cos⁻¹(0) using principal values.Inverse trigonometric functions are sometimes called which of these?Which country is credited with starting the study of trigonometry?