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Test: Inverse Trigonometry- 2 - JEE MCQ


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25 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Inverse Trigonometry- 2

Test: Inverse Trigonometry- 2 for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Inverse Trigonometry- 2 questions and answers have been prepared according to the JEE exam syllabus.The Test: Inverse Trigonometry- 2 MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Inverse Trigonometry- 2 below.
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Test: Inverse Trigonometry- 2 - Question 1

cos2θ is not equal to

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 1

cos 2θ is equal to cos2θ - sin2θ = 2cos2θ - 1

Test: Inverse Trigonometry- 2 - Question 2

 is equal to 

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 2

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

Test: Inverse Trigonometry- 2 - Question 3

2cos−1x = cos−1(2x2−1)holds true for all

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 3

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

Test: Inverse Trigonometry- 2 - Question 4

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 4

none of these  : 7/25

Test: Inverse Trigonometry- 2 - Question 5

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

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 5

(Sin A + Cos A)2 = sin2A + cos2A + 2 sinAcosA

1 = 1 + Sin 2A

so, Sin 2A = 0

Hence A = 0 

Test: Inverse Trigonometry- 2 - Question 6

When x = π/2, then tan x, is

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 6

tan π/2 = n.d.i.e. not defined.

Test: Inverse Trigonometry- 2 - Question 7

The value of the expression sinθ+cosθ lies between

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 7

Minimum value   

and maximum value = 

Test: Inverse Trigonometry- 2 - Question 8

cos−1(cosx) = x is satisfied by ,

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 8

cos−1(cosx) = x if, 
0⩽x⩽ π i.e. if , x∈ [0,π]

Test: Inverse Trigonometry- 2 - Question 9

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 9








 

Test: Inverse Trigonometry- 2 - Question 10

If ƒ(x) = tan(x), then f-1(1/√(3)) =

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 10

Let F(x) = tanx = y
f(-1) = tany = x
f(-1)(1/√3), tany = 1/√3
y = tan-(1/√3)
=π/6

Test: Inverse Trigonometry- 2 - Question 11

tan x is periodic with period 

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 11

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

Test: Inverse Trigonometry- 2 - Question 12

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 12

Test: Inverse Trigonometry- 2 - Question 13

 is equal to 

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 13




Test: Inverse Trigonometry- 2 - Question 14

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 14


Test: Inverse Trigonometry- 2 - Question 15

 

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 15

The correct option is B.

Test: Inverse Trigonometry- 2 - Question 16

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

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 16

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

Test: Inverse Trigonometry- 2 - Question 17

The range of tan−1 x is

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 17

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

Test: Inverse Trigonometry- 2 - Question 18

The value of   is (a, b > 0)

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 18



Test: Inverse Trigonometry- 2 - Question 19

The solution of the equation 

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 19



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

Test: Inverse Trigonometry- 2 - Question 20

 is equal to 

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 20

= tan-1 a - tan-1 b + tan-1c + tan-1c - tan-1a

Test: Inverse Trigonometry- 2 - Question 21

sin2250+sin2650 is equal to

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 21

sin2250 + sin2650 = cos2650 + sin2650 = 1

Test: Inverse Trigonometry- 2 - Question 22

If θ = tan−1x then sin 2θ is equal to

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 22

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

Test: Inverse Trigonometry- 2 - Question 23

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

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 23

Test: Inverse Trigonometry- 2 - Question 24

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 24

Test: Inverse Trigonometry- 2 - Question 25

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

Detailed Solution for Test: Inverse Trigonometry- 2 - Question 25

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