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Mere Teacher · Previous Year Questions
JEE Main Mathematics · Inverse Trigonometric Functions · Set 2 (Q31-60)
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31.
If α≤2sin−1x+cos−1x≤β, then
(1)α=2−π,β=23π
(2)α=0,β=2π
(3)α=2−π,β=2π
(4)α=0,β=π
32.
If θ∈(−2π,2π), then cos−1(sinθ) is equal to
(1)2π−θ
(2)θ−2π
(3)2π+θ
(4)π+2θ
33.
If 0<x<21 and αsin−1x=βcos−1x, then a value of sin(α+β2πα)
(1)4(1−x2)(1−2x2)
(2)4x(1−x2)(1−2x2)
(3)2x(1−x2)(1−4x2)
(4)4(1−x2)(1−4x2)
34.
The value of tan(2tan−1(53)+sin−1(135))is equal to:
(1)69−181
(2)21220
(3)76−291
(4)63151
35.
For α,β,γ=0. If sin−1α+sin−1β+sin−1γ=π and (α+β+γ)(α−γ+β)=3αβ, then γ equal to
(1)23
(2)21
(3)223−1
(4)3
36.
The value of sin−1(1312)−sin−1(53) is equal to :
(1)π−sin−1(6563)
(2)2π−sin−1(6556)
(3)2π−cos−1(659)
(4)π−cos−1(6533)
37.
The value of cos(sin−13π+cos−13π)
(1)1
(2)-1
(3)Does not exist
(4)0
38.
If coscot−1(21)=cot(cos−1x), then the value of x is
(1)61
(2)12−1
(3)62
(4)6−2
39.
(x−1)(x+3)3x+1=x−1A+x+3B, then sin−1BA=
(1)4π
(2)2π
(3)3π
(4)6π
40.
Let S be the set of all solutions of the equation cos−1(2x)−2cos−1(1−x2)=π,xϵ(−21,21) Then ∑2sin−1(x2−1) is equal to
(1)0
(2)3−2π
(3)π−sin−1(43)
(4)π−2sin−1(43)
41.
sec(tan−12y)=
(1)24+y2
(2)24−y2
(3)24+y2
(4)24−y2
42.
If α>β>γ>0, then the expression cot−1(β+α−β1+β2)+cot−1(γ+β−γ1+γ2)+cot−1(α+γ−α1+α2) is equal to:
(1)π
(2)0
(3)2π−(α+β+γ)
(4)3π
43.
cos−1(cos(−5)) + sin−1(sin(6)) − tan−1(tan(12)) is equal to : (The inverse trigonometric functions take the principal values)
(1)3π − 11
(2)4π − 9
(3)4π − 11
(4)3π + 1
44.
If x=nπ,x=(2n+1)2π,n∈Z then tan−1(cotx)+cot−1(tanx)sin−1(cosx)+cos−1(sinx)=
(1)6π
(2)2π
(3)3π
(4)1
45.
cos(2sin−143+cos−143)=
(1)4−3
(2)53
(3)43
(4)does not exist
46.
Let x=nm(m,n) are co-prime natural numbers) be a solution of the equation cos(2sin−1x)=91 and let α,β(α>β) be the roots of the equation mx2−nx−m+n=0. Then the point (α,β) lies on the line
(1)3x+2y=2
(2)5x−8y=−9
(3)3x−2y=−2
(4)5x+8y=9
47.
Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of 16((sec−1x)2+(cosec−1x)2) is:
(1)24π2
(2)22π2
(3)31π2
(4)18π2
48.
sin(tan−154+tan−134+tan−191−tan−171) is equal to
(1)21
(2)21
(3)23
(4)1
49.
If ' x ' takes negative permissible value, then sin−1x is equal to
(1)π−cos−11−x2
(2)cos−11−x2
(3)−cos−11−x2
(4)cos−1x2−1
50.
The domain of f(x)=cos−1(2x−3)−log10(4−x) is
(1)(1,4)
(2)[1,4)
(3)(1,4]
(4)[1,4]
51.
If tan−1x=4π−tan−1(31), then x is
(1)31
(2)21
(3)41
(4)61
52.
sech−1(21)+cosech−1(−1)=
(1)0
(2)2+1
(3)2
(4)2−1
53.
cos(sin−153+sin−1135+sin−16533) is equal to:
(1)1
(2)0
(3)6532
(4)6533
54.
The value of tan−1(yx)−tan−1(x+yx−y),x,y>0 is
(1)4π
(2)−4π
(3)2π
(4)−2π
55.
Let k>0 and t=sech−1(21)−cosech−1(k3). 3et=2+3, then k is equal to
(1)2
(2)4
(3)33
(4)32
56.
If θ=2tan−181+2tan−151+tan−171 and tan2θ=m+n, where m and n are positive integers such that m<n, then (mn+nm)m+n is equal to
(1)18
(2)27
(3)25
(4)36
57.
For x ∈ (-1,1], the number of solutions of the equation sin−1 x = 2 tan−l x is equal to
58.
If for some α,β; α≤β, α+β=8 and sec2(tan−1α)+cosec2(cot−1β)=36, then α2+β is .
59.
If y=∑k=16kcos−1(53coskx−54sinkx), then dxdy at x=0 is:
60.
If the sum of all the solutions of tan−1(1−x22x)+cot−1(2x1−x2)=3π −1<x<1,x=0 is α−34, then α is equal to
