JEE Advanced Level Test: Fundamentals of Trigonometric - JEE MCQ

# JEE Advanced Level Test: Fundamentals of Trigonometric - JEE MCQ

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## 30 Questions MCQ Test Chapter-wise Tests for JEE Main & Advanced - JEE Advanced Level Test: Fundamentals of Trigonometric

JEE Advanced Level Test: Fundamentals of Trigonometric for JEE 2024 is part of Chapter-wise Tests for JEE Main & Advanced preparation. The JEE Advanced Level Test: Fundamentals of Trigonometric questions and answers have been prepared according to the JEE exam syllabus.The JEE Advanced Level Test: Fundamentals of Trigonometric MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Advanced Level Test: Fundamentals of Trigonometric below.
JEE Advanced Level Test: Fundamentals of Trigonometric - Question 1

### The maximum value of (cos α1), (cos α2),........(cos αn) under the restrictions  0 < α1, α2,....... and (cot α1), (cot α2),..........(cot αn) = 1 is

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 1

(cot α1) (cot α2)........... cot αn =1
(cos α1) (cos α2) .......... cos αn = (sin α1) (sin α2) .......... sin αn
Let y = (cos α1) (cos α2) ................ (cos αn) (to be maximum)
Squaring y2 = (cos2 α1) (cos2 α2) ................ (cos2 αn)
= (cos α1 sin α1) (cos α2 sin α2) ................ (cos αn sin αn)    using equation 1

[sin 2α1. sin2α2 .........sin 2αn]
0 < sin2α1. sin2α2 .........sin 2αn < 1

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 2

### The number of integral values of k for which the equation 7 cos x + 5 sin x = 2k + 1 has a solution, is

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 2

We know, < a sinx + bcos x
7cosx+5sinx

Since k is integer,   -9 < 2k + 1 < 9 ⇒ -10 < 2k < 8 ⇒ -5 < k < 4
⇒ Number of possible integer values of k = 8.

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JEE Advanced Level Test: Fundamentals of Trigonometric - Question 3

### If cos θ  then tan θ/2 equals

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 3

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 4

The  value of sin310o + sin350o - sin370o is equal to

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 4

sin310° + sin350° - sin370°
= 1/4 [(3 sin 10° - sin 30°) + (3 sin 50° - sin 150°) - (3 sin 70° - sin 210°)]

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 5

If xy + yz + zx = 1 then

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 5

put x = tan A, y = tan B, z = tan C
tan A tan B + tan B tan C + tan C tan A = 1
tan C [tan A + tan B] = 1– tan A tan B

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 6

Let n be a positive integer such that

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 6

since n is appositive integer

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 7

If sin θ + sin 2θ + sin 3θ = sin α and cos θ + cos 2θ + cos 3θ = cos α , then θ is equal to

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 7

sinθ+sin3θ+sin2θ=sinα
⇒ 2 sin 2θ cosθ + sin 2θ = sin α

⇒ sin 2θ(2 cos θ +1) = sin α........(1)
Now cos θ + cos 3θ + cos 2θ = cos α cos 2θ (2 cos θ + 1) = cos α. ....(2)
From (1) and (2), tan 2θ = tan α ⇒ 2θ = α ⇒θ = α/2

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 8

If π/2 < α < π and 3π/2 < β < 2π , sinα = 15/17 and tanβ = , then sin (β - α) is

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 8

So, sin (β - α) = sin β.cosα - cos β.sin a

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 9

The expression  is equal to

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 9

3[cos4 α + sin4 α] - 2[cos6 α + sin6 α]
= 3[(cos2 α + sin2 α)2 - 2sin2α.cosα]- 2
[(sin2 α + cos2 α)3 - 3 sin2 α.cos2 α.(sin2 α + cosa)]
= 3[1 - 2sin2 α.cos2 α] - 2[1 - 3 sinα.cos2 α] = 3 - 2 = 1

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 10

If tan x + tan (x + π/3) + tan (x + 2π/3) = 3, then

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 10

The given equation can be written as

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 11

If sin A = sin B and cos A = cos B, A > B, then

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 11

sin A = sin B ⇒ sin A - sim B = 0
...........(1)
and cos A = cos B ⇒ cos B - cos A = 0
..........(2)

Equations (1) and (2) are simultaneously true if sin (1/2) (A – (B) = 0,
while the other factors sin (1/2) (A+ (B) and cos (1/2) (A + (B) cannot both be zero simultaneously.

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 12

In a triangle ABC if A = π/4 and tanB tanC = K, then K must satisfy.

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 12

In a ΔABC, we know that
tanA + tanB + tanC = tanA tanB tanC
∴ tanB + tanC = tanA(tanBtanC – 1)

⇒ tan2 B - (K - 1) tan B + K = 0
For real values of tan B, Disc.
(K – 1)2 – 4K > 0
K2 – 6K + 1 >

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 13

The number of pairs (x, y) satisfying the equations sin x + sin y = sin (x + y) and |x| + |y| = 1 is

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 13

sin x + sin y = sin (x + y)

The possibilities are x = 0 or, y = 0 or, x + y = 0
When x = 0 , y = ±1
When y = 0 , x = ±1

Clearly, there are 6 pairs.

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 14

If θ = 2π/7, then the value of tan θ tan 2θ + tan 2θ tan 4θ + tan 4θ tan θ is

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 14

Put θ = A, 2θ = B, 4θ = c
∴ A + B + C = 7θ = 2π

But cos (A + B + C)
= cos A cos B cos C - ∑ sin A sin B cosC
∴ sin A sin Bsin C = cos A cos Bcos C - cos 2π

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 15

Let A/2 = -140° then the value of

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 15

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 16

The value of

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 16

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 17

If sin2 (θ - α) cos α = cos2 (θ - α) sin α = m sin α cos α then

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 17

sin2 (θ - α) cos α = cos2 (θ - α) sin α = m sin α cos α

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 18

If 0 < θ < π then

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 18

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 19

1 + sec 200 = cot x0.cot y0 then x+y may be

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 19

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 20

The value of cot

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 20

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 21

cos100.cos 200.cos 400 is equal to

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 21

cos100.cos 200.cos 400

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 22

If cos 250 + sin 250 = K, then cos 500 is equal to

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 22

cos 250 + sin 250 = K
Squaring,
1 + sin 500 = K2
sin 500 = K-1

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 23

If cos x = tan y, cos y = tan z, cos z = tan x then the value of sin x is

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 23

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 24

Which of the following is rational ?

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 24

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 25

If α + β + γ = π and tan  then the value of cos α + cos β + cos γ is

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 25

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 26

The value of

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 26

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 27

If sin x + cosec x + tan y + cot y = 4 where x and then tan y/2 is a root of the equation

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 27

sin x + cosec x > 2 (using A.M > G.M)
Also tan y + cot > 2
So, sin x + cosec x + tan y + cot y = 4 is possible when

So, tan y/2 is a root of the equation α2 + 2α - 1 = 0

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 28

If circumference of a circle is divided into 360 congruent parts, angle subtended by one part at center of circle is called

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 29

cot B = 2 tan A - B) ⇒ 2 tan B + cot B =

Detailed Solution for JEE Advanced Level Test: Fundamentals of Trigonometric - Question 29

⇒ cot B + tan A = 2 tan A – 2 tan B
⇒ 2 tan B + cot B = tan A

JEE Advanced Level Test: Fundamentals of Trigonometric - Question 30

If log1/3 (5x – 1) > 0 then x belongs to

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