Practice question On INVERSE TRIGONOMETRY for IITJEE , Airforce And NDA 31-45 (Set 3 )

Inverse Trigonometry

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Question no. 31

The value of cot(cosec^-15/3 + tan^-12/3)

looks_one 4/17

looks_two 5/17

looks_3 6/17

looks_4 3/17

Option looks_3 6/17

Solution :

Question no. 32

The Value of is

looks_one π/4

looks_two π/2

looks_3 π/3

looks_4 π/6

option looks_4 π/6

Solution :

Question no. 33

If x,y ,z are in A.P. and tan^-1x , tan^-1y, tan^-1z are also in A.P. , then :

looks_one x=y=z

looks_two 2x=3y=6z

looks_3 6x=3y=2z

looks_4 6x=4y=3z

option looks_one x=y=z

Solution :
x,y ,z are in A.P.
2y = x + z
tan^-1x , tan^-1y, tan^-1z are also in A.P.
2tan^-1y = tan^-1x + tan^-1z

only x = y = z satisfy it.

Question no. 34

Let x ∈(0,1) , the set of all x such that sin^-1x > cos^-1x is the interval

looks_one (1/2, 1/√2)

looks_two (1/√2, 1)

looks_3 (0,1)

looks_4 (0,√3/2)

option looks_two (1/√2, 1)

Solution :
sin^-1x > cos^-1x
sin^-1x > π/2 - sin^-1x
2sin^-1x > π/2
sin^-1x > π/4
x > 1/√2

Question no. 35

If , tanS=

looks_one 20/(401+20n)

looks_two n/(n² +20n+1)

looks_3 20/(n² +20n+1)

looks_4 n/(401+20n)

option looks_3 20/(n² +20n+1)

very soon

Question no. 36

The principal value of tan^-1(cot43π/4) is

looks_one 3π/4

looks_two -3π/4

looks_3 π/4

looks_4 -π/4

option looks_4 -π/4

Solution :

Question no. 37

If , x>1 , then f(5) is

looks_one π/2

looks_two π

looks_3 4tan^-15

looks_4 tan^-1(65/156)

option looks_3 4tan^-15

Solution :

Question no. 38

If sin^-1x - cos^-1x = π/6, then x=

looks_one 1/2

looks_two √3/2

looks_3 -1/2

looks_4 none of these

option looks_two √3/2

Solution :
sin^-1x - cos^-1x = π/6
sin^-1x - (π/2 - sin^-1x ) = π/6
2 sin^-1x = π/2 + π/6
2 sin^-1x = 2 π/3
sin^-1x = π/3
x = √3/2

Question no. 39

The number of solution of the equation tan^-12x + tan^-13x = π/4 is

looks_one 2

looks_two 3

looks_3 1

looks_4 none of these

option looks_one 2

Solution :
tan^-12x + tan^-13x = π/4
tan^-1(5x/(1-6x²)) = π/4
5x/(1 - 6x²) = 1
6x² + 5x - 1 = 0
(x+1)(6x-1) = 0
x = -1 , 1/6

Question no. 40

If α= tan^-1(tan5π/4) and β=tan^-1(-tan2π/3)

looks_one 4α=3β

looks_two 3α=4β

looks_3 α - β= 7π/12

looks_4 none of these

option looks_one 4α=3β

Solution :

Question no. 41

If tan^-1(cotB)= 2B , then B=

looks_one ∓π/6

looks_two ∓π/4

looks_3 ∓π/3

looks_4 none of these

option looks_one ∓π/6

Solution :
tan^-1(cotB) = 2B
cot B = tan(2B)
π/2 -B = nπ + 2B
3B = π/2 - nπ
For n = 0 , B = π/6
For n = 1 , B = -π/6

Question no. 42

cot(π/4-2cot^-13) =

looks_one 7

looks_two 6

looks_3 5

looks_4 none of these

Option looks_one 7

Solution :

Question no. 43

The value of sin(0.25sin^-1√63/8) is

looks_one 1/√2

looks_two 1/√3

looks_3 1/2√2

looks_4 1/3√3

Option looks_3 1/2√2

Solution :

Question no. 44

If sin^-1x + 4cos^-1x = π, then the value of x is

looks_one 3/2

looks_two 1/√2

looks_3 √3/2

looks_4 2/√3

option looks_3 √3/2

Solution :
sin^-1x + 4cos^-1x = π
π/2 - cos^-1x + 4cos^-1x = π
3cos^-1x = π/2
cos^-1x = π/6
x = √3/2

Question no. 45

If cos^-1(x/2) +cos^-1(y/3)=α , then 9x² -12xycosα +4y² is

looks_one 36

looks_two 36sin²α

looks_3 -36sin²α

looks_4 36cos²α

option looks_two 36sin²α

Solution :
cos^-1(x/2) +cos^-1(y/3)=α

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