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This mock test of Test: Inverse Trigonometry- 2 for JEE helps you for every JEE entrance exam.
This contains 25 Multiple Choice Questions for JEE Test: Inverse Trigonometry- 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

cos2θ is not equal to

Solution:

cos 2θ is equal to cos^{2}θ - sin^{2}θ = 2cos^{2}θ - 1

QUESTION: 2

is equal to

Solution:

sin^{-1}√3/5 = A

Sin A = √3/5 , cos A = √22/5

Therefore Cos^{-1}√3/5 = B

Cos B = √3/5 , sin B = √22/5

sin(A+B) = sinA cosB + cosA sinB

= √3/5 * √3/5 + √22/5 * √22/5

= 3/25 * 22/25

= 25/25

= 1

QUESTION: 3

2cos^{−1}x = cos^{−1}(2x^{2}−1)holds true for all

Solution:

This is true for all real values of x ∈ [0,1].

QUESTION: 4

Solution:

none of these : 7/25

QUESTION: 5

If sin A + cos A = 1, then sin 2A is equal to

Solution:

(Sin A + Cos A)^{2} = sin^{2}A + cos^{2}A + 2 sinAcosA

1 = 1 + Sin 2A

so, Sin 2A = 0

Hence A = 0

QUESTION: 6

When x = π/2, then tan x, is

Solution:

tan π/2 = n.d.i.e. not defined.

QUESTION: 7

The value of the expression sinθ+cosθ lies between

Solution:

Minimum value

and maximum value =

QUESTION: 8

cos^{−1}(cosx) = x is satisfied by ,

Solution:

cos^{−1}(cosx) = x if,

0⩽x⩽ π i.e. if , x∈ [0,π]

QUESTION: 9

Solution:

QUESTION: 10

If ƒ(x) = tan(x), then f^{-1}(1/√(3)) =

Solution:

Let F(x) = tanx = y

f^{(-1)} = tany = x

f^{(-1)}(1/√3), tany = 1/√3

y = tan^{-(1/√3)}

=π/6

QUESTION: 11

tan x is periodic with period

Solution:

The values of tan x repeats after an interval of π.

QUESTION: 12

Solution:

QUESTION: 13

is equal to

Solution:

QUESTION: 14

Solution:

QUESTION: 15

Solution:

**The correct option is B.**

QUESTION: 16

The period of the function f(x) = tan 3x is

Solution:

f(x) = tan 3x, as the period of tan x = π. 3x = x = π/3.

QUESTION: 17

The range of tan^{−1} x is

Solution:

The range of tan^{−1}x is given by -π/2 to π/2

QUESTION: 18

The value of is (a, b > 0)

Solution:

QUESTION: 19

The solution of the equation

Solution:

But , x= -1/2 does not satisfy the given equation.

QUESTION: 20

is equal to

Solution:

= tan^{-1} a - tan^{-1 }b + tan^{-1}c + tan^{-1}c - tan^{-1}a

QUESTION: 21

sin^{2}25^{0}+sin^{2}65^{0} is equal to

Solution:

sin^{2}25^{0} + sin^{2}65^{0} = cos^{2}65^{0} + sin^{2}65^{0} = 1

QUESTION: 22

If θ = tan^{−1}x then sin 2θ is equal to

Solution:

As we know that : sin 2θ = , now if θ = tan^{-1}x ⇒ x = tan θ ⇒ sin 2θ =

QUESTION: 23

if x > 0, then tan^{-1}x + tan^{-1}(1/x) is equal to

Solution:

QUESTION: 24

Solution:

QUESTION: 25

If and x + y + z = xyz, then a value of tan^{−1}x+tan^{−1}y+tan^{−1}z is

Solution:

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