68 free MCQs on Inverse Trigonometric Functions, each with its own worked answer and explanation. Restricting trig functions to make them invertible, the principal value branches of sin-inverse, cos-inverse, tan-inverse, and friends, and the key identities relating them.
Take the timed Inverse Trigonometric Functions chapterwise test →68 practice questions on Inverse Trigonometric Functions, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Inverse Trigonometric Functions notes.
The graph of sin⁻¹x is confined to a narrow domain [-1,1] (since sine itself only takes values in that range) and range [-π/2,π/2] (the principal value branch chosen to make sine one-one and invertible there).
Q1.
The principal value range of sin-1 x is:
Q2.
The principal value range of cos-1 x is:
Q3.
The principal value range of tan-1 x is:
Q4.
Why must the domain of sin x be restricted before defining sin-1 x?
Q11.
The domain of sec-1 x is:
Q14.
The range of cot-1 x excludes which value?
Q18.
The function sin⁻¹(x) is also written as:
Q19.
The value of sin⁻¹(1) is:
Q20.
The domain of the function sin⁻¹(x) is:
Q26.
Simplify 2 tan-1(1/2) using the double angle identity 2tan-1 x = sin-1(2x/(1+x<sup>2</sup>)).
Q27.
Express cot-1(-x) in terms of cot-1 x.
Q28.
If sin-1 x = pi/3, find the value of cos-1 x.
Q29.
Solve for x: tan-1(2x) + tan-1(3x) = pi/4.
Q30.
Express tan-1(cos x / (1 + sin x)) in simplified principal value form for x in (-pi/2, pi/2).
Q34.
Simplify 2 tan-1(1/3) using the double angle identity 2tan-1 x = tan-1(2x/(1-x<sup>2</sup>)).
Q35.
The principal value range of sin⁻¹(x) is:
Q36.
The principal value range of cos⁻¹(x) is:
Q41.
Solve: sin-1(x) + sin-1(2x) = pi/3. Approximate the smaller positive root region check, given x must satisfy domain constraints.
Q42.
Simplify tan-1[(sqrt(1+x<sup>2</sup>) - 1)/x] for x > 0 in terms of tan-1 x.
Q43.
If cos-1 x + cos-1 y + cos-1 z = 3pi (the maximum possible sum), what must be true of x, y, z?
Q45.
Find the value of cos[2cos-1(3/5) ] using the double angle formula cos(2theta) = 2cos<sup>2</sup>(theta) - 1.
Q46.
Solve for x: 2 tan-1(cos x) = tan-1(2 cosec x), for x in (0, pi/2).
Q47.
If tan-1 x + tan-1 y + tan-1 z = pi and x, y, z > 0, which relation among x, y, z holds?
Q48.
Evaluate sin[cos-1(4/5) + tan-1(2/3)] using compound angle expansion.
Q49.
If sin<sup>-1</sup>(x) - cos<sup>-1</sup>(x) = pi/6, find the value of x.
Q50.
Find the value of tan[2 tan<sup>-1</sup>(1/5) - pi/4].
Q56.
The expression 2 tan⁻¹(x) can be written as tan⁻¹ of:
Q57.
The value of cos(cos⁻¹(0.5)) is:
Q58.
For suitable x, sec⁻¹(x) + cosec⁻¹(x) equals:
Q65.
The principal-value range of arcsec x is:
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