Trigonometric Ratios, Functions & Equations - 1 - JEE MCQ

# Trigonometric Ratios, Functions & Equations - 1 - JEE MCQ

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## 30 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Trigonometric Ratios, Functions & Equations - 1

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

### The angles of a triangle are as 1 : 2 : 7, then ratio of greatest side to least side is

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 1

Let the angles be x, 2x, and 7x respectively.
⇒ x + 2x + 7x = 180° [angle sum property of triangle]
⇒ 10x = 180°
⇒ x = 18°
Hence, the angles are: 18°,36°,126°

⇒ Greatest Side = K sin 126°
⇒ Smallest side = K sin 18°
So, required ratio =K sin 126°/ K sin 18°
= sin(90°+36°)/sin18°= cos36°/sin18°    [sin(90°+x)=cosx]
= (√5+1)/(√5−1)

Trigonometric Ratios, Functions & Equations - 1 - Question 2

### If the sides of a triangle are 13, 7, 8 the greatest angle of the triangle is

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 2

a = 13, b = 7, c = 8

By cosine formula,

⇒ A = 120º = 2π/3

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Trigonometric Ratios, Functions & Equations - 1 - Question 3
Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 3

Trigonometric Ratios, Functions & Equations - 1 - Question 4

If a = 4, b = 3 and A = 60, then c is a root of the equation

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 4

c− 7 = 3c ⇒ c− 3c − 7 = 0

Replace c by x : x2 - 3x - 7 = 0

Trigonometric Ratios, Functions & Equations - 1 - Question 5

If cos A + cos B = , then the sides of the triangle ABC are in

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 5

cos A + cos B = 4 sin2(C/2​)
⇒ 2 cos (A+B)/2​ cos (A−B)/2 ​= 4 sin2(C/2​)

∵ A + B + C = π ⇒ A + B = π − C

⇒ cos (π−C)/2 ​cos (A−B)/2 ​= 2 sin2(C/2​)
⇒ sin C/2 ​cos (A−B)/2 ​= 2 sin2(C/2​)
⇒ cos (A−B)/2 = 2 sin (C/2​)
⇒ cos C/2 ​cos (A−B)/2 = 2 sin (C/2​) cos (C/2)​
⇒ cos (π−(A+B)​)/2 cos (A−B)/2 = sin C
⇒ 2 sin (A+B)/2 ​cos (A−B)/2​ = sin C
⇒ sin A + sin B = 2 sin C

∵ a/sinA​ = b/sinB​ = c/sinC​ = k
⇒sinA = ak, sin B = bk , sin C = ck

⇒ ak + bk = 2(ck)
⇒ a+b=2c

Therefore the sides of triangle a,b,c are in A.P.

Trigonometric Ratios, Functions & Equations - 1 - Question 6

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 6

Trigonometric Ratios, Functions & Equations - 1 - Question 7

Number of solutions of the equation cos6x + tan2x + cos6x . tan2x = 1 in the interval [0, 2π] is-

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 7

Trigonometric Ratios, Functions & Equations - 1 - Question 8

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 8

Trigonometric Ratios, Functions & Equations - 1 - Question 9

If tan(cot x) = cot(tan x), then sin 2x =

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 9

Trigonometric Ratios, Functions & Equations - 1 - Question 10

If m and n(> m) are positive integers, the number of solutions of equation n|sin x| = m|cos x| in [0, 2π] is -

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 10

Trigonometric Ratios, Functions & Equations - 1 - Question 11

sin 3 θ = 4 sin θ sin 2 θ sin 4 θ in 0 ≤ θ ≤ π has

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 11

Trigonometric Ratios, Functions & Equations - 1 - Question 12

The general solution to the equation tan 2θ. tan θ = 1 is

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 12

Trigonometric Ratios, Functions & Equations - 1 - Question 13

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 13

Trigonometric Ratios, Functions & Equations - 1 - Question 14

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 14

Trigonometric Ratios, Functions & Equations - 1 - Question 15

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 15

Trigonometric Ratios, Functions & Equations - 1 - Question 16

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

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 16

Trigonometric Ratios, Functions & Equations - 1 - Question 17

If the equation sin θ (sin θ + 2 cos θ) = a has a real solution, then the shortest interval containing all possible values of ‘a’ is

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 17

Trigonometric Ratios, Functions & Equations - 1 - Question 18

The number of solutions of the equation  2(sin4 2x + cos4 2x) + 3 sin2 x cos2 x = 0 is

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 18

Trigonometric Ratios, Functions & Equations - 1 - Question 19

Solution to the equation tan pθ = cot qθ is

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 19

Trigonometric Ratios, Functions & Equations - 1 - Question 20

Range of sin2 x + 3 sin x + 2 is

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 20

Trigonometric Ratios, Functions & Equations - 1 - Question 21

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 21

Trigonometric Ratios, Functions & Equations - 1 - Question 22

Find the number of principal solution of the equation tan (7π cos x) = cot (7π sin x).

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 22

Trigonometric Ratios, Functions & Equations - 1 - Question 23

The solution set of (2 cos x– 1) (3 + 2 cos x) = 0 in the interval 0 ≤ x ≤ 2π is -

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 23

Trigonometric Ratios, Functions & Equations - 1 - Question 24

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 24

Trigonometric Ratios, Functions & Equations - 1 - Question 25

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Trigonometric Ratios, Functions & Equations - 1 - Question 26

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 26

Trigonometric Ratios, Functions & Equations - 1 - Question 27

If sin2 x + sin xy = – 1, then  the value of x, y is

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 27

Trigonometric Ratios, Functions & Equations - 1 - Question 28

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 28

Trigonometric Ratios, Functions & Equations - 1 - Question 29

Solution of the inequality sin2x – 5sinx + 6 < 0 is

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 29

Trigonometric Ratios, Functions & Equations - 1 - Question 30

If cos x . cos y = 1, then the value of  x and y  is

Detailed Solution for Trigonometric Ratios, Functions & Equations - 1 - Question 30

## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests
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## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests