CBSE Class 12 Mathematics Inverse Trigonometric Functions MCQs Set D

Question: cot^–1(ab + 1/a − b) + cot^–1(bc + 1/b − c) + cot^–1(ca + 1/c − a) is equal to …
(a) 0
(b) π/4
(c) 1
(d) 5
Answer: a

Question: If sin ^–1 (6x/1+9x²) = 2tan ^–1(ax), then a =
(a) 3
(b) 8
(c) 6
(d) 9
Answer: a

Question: If xy + yz + zx = 1, then :
(a) tan^–1 x +tan^–1 y + tan^–1 z = 0
(b) tan^–1 x + tan^–1 y +tan^–1 z = π
(c) tan^–1 x +tan^–1 y +tan^–1 z = π/4
(d) tan^–1 x + tan^–1 y + tan^–1 z = π/2
Answer: d

Question: If tan^–13 + tan^–1 x = tan^–18, then x =
(a) 5
(b) 1/5
(c) 5/14
(d) 14/5
Answer: b

Question: If sin^–1(1– x ) – 2 sin^–1 x = π/2 ,then x equals
(a) 0,−1/2
(b) 0, 1/2
(c) 0
(d) None of these
Answer: b

Question: Principal value of sec^–1(2) is equal to
(a) π/6
(b) π/3
(c) 2π/3
(d) 5π/3
Answer: b

Question: cos^–1(1/2) + sin^–1(1/2) + tan^–11/√3 is equal to
(a) π
(b) π/3
(c) 4π/3
(d) 3π//4
Answer: a

Question: If sin(sin^–11/5 + cos^–1x 1) = 1, then the value of x is
(a) –1
(b) 2/5
(c) 1/3
(d) 1/5
Answer: d

Question: If tan⁻¹(x +1) + cot⁻¹(x −1) = sin⁻¹ 4/5 + cos⁻¹ 3/5 then x has the value :
(a) 4√3/7
(b) 4√7/3
(c) 14√3
(d) 6√7
Answer: a

Question: If sin^–1(1/5) + sec^–1(2) + 2tan^–1(1/√3) + sec^–1(5) + sin^–1(1/2) + 2tan^–1(√3) = kπ, then k =
(a) 1
(b) 2
(c) 4
(d) 5
Answer: b

Question: If cos^–1 (1/√5) = θ , then the value of cosec^–1 (√5) is
(a) (π/2) + θ
(b) (π/2) − θ
(c) π/2
(d) − θ
Answer: b

Question: sin {2cos^–1 (–3/5)} is equal to
(a) 6/25
(b) 24/25
(c) 4/5
(d) – 24/25
Answer: d

Question: The value of tan^–1(1/2) + tan^–1(1/3) + tan^–1(7/8) is
(a) tan^–1(7/8)
(b) cot^–1 (15)
(c) tan^–1(15)
(d) tan^–1(25/24)
Answer: c

Question: The value of tan (cos^–14/5 + tan^–12/3) =
(a) 6/17
(b) 7/16
(c) 16/7
(d) None of these
Answer: d

Question: The value of cos–1 (cos3π/2) is equal to
(a) π/6
(b) 3π/2
(c) 5π/2
(d) 7π/2
Answer: a

Question: If |x| ≤ 1, then 2 tan^–1x + sin^–1 (2x/1+ x²) is equal to
(a) 4 tan^–1x
(b) π/2
(c) 0
(d) π
Answer: a

Question: The value of cos^–1(cos5π/3) + sin^–1(sin5π/3) is
(a) π/2
(b) 5π/3
(c) 10π/3
(d) 0
Answer: d

Question: The value of expression 2sec^–1 2+ sin^–1(1/2) is
(a) π/6
(b) 5π/6
(c) 7π/6
(d) 1
Answer: b

Question: Domain of cos^–1[x] is
(a) [–1, 2]
(b) [–1, 2)
(c) (–1, 2]
(d) None of these
Answer: b

Question: If cos^–1x + cos^–1y + cos^–1z = 3π then xy + yz + zx is equal to :
(a) 1
(b) 0
(c) –3
(d) 3
Answer: d

Question: If sin (cot^–1(1 +x)) = cos (tan^–1x), then x =
(a) 1/2
(b) 1
(c) 0
(d)−1/2
Answer: d
 

ASSERTION- REASON TYPE QUESTIONS

(a) Assertion is correct, reason is correct; reason is a correctexplanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Question:
Assertion: If x < 0, tan^–1 x + tan ^–1 (1/x) = π/2
Reason: tan^–1x + cot ^–1 x = π/2, ∀ x ∈ R
Answer: d

Question:
Assertion: 2tan^–11/2 + tan^–11/7 = tan^–1 31/17.
Reason: 2tan^–1x = tan^–1 (2x/1 − x²) if –1 < x < 1.
Answer: a

Question:
Assertion: cosec^–1(3/2) + cos^–1(2/3) − 2cot^–1(1/7) − cot^–1(7) is equal to cot^–17.
Reason: sin^–1x + cos^–1x = π/2 , tan^–1 x + cot^–1 x = π/2
cosec^–1x = sin^–1(1/x), cot^–1(x) = tan^–1(1/x)
Answer: d

Question:
Assertion : The value of tan^–1(3/4) + tan^–1(1/7) is π/4
Reason : If x > 0, y > 0 then tan^–1(x/y) + tan^–1(y − x/y + x) = π/4
Answer: d

Question:
Assertion: sin^–1 8/17 + sin^–1 3/5 = sin^–1 77/85
Reason: tan^–1x + tan^–1y = tan^–1(x + y/1 − xy)
Answer: b