JEE Advanced Level Test: Trigonometric Equations- 2 - Airforce X Y / Indian Navy SSR MCQ

# JEE Advanced Level Test: Trigonometric Equations- 2 - Airforce X Y / Indian Navy SSR MCQ

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## 25 Questions MCQ Test - JEE Advanced Level Test: Trigonometric Equations- 2

JEE Advanced Level Test: Trigonometric Equations- 2 for Airforce X Y / Indian Navy SSR 2024 is part of Airforce X Y / Indian Navy SSR preparation. The JEE Advanced Level Test: Trigonometric Equations- 2 questions and answers have been prepared according to the Airforce X Y / Indian Navy SSR exam syllabus.The JEE Advanced Level Test: Trigonometric Equations- 2 MCQs are made for Airforce X Y / Indian Navy SSR 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for JEE Advanced Level Test: Trigonometric Equations- 2 below.
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JEE Advanced Level Test: Trigonometric Equations- 2 - Question 1

### If 20 sin2θ + 21 cos θ – 24 = 0 & 7π/4 < θ < 2π then the values of cot θ/2 is

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 2

### The general solution of the equation tan x + tan  + tan  = 3 is

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JEE Advanced Level Test: Trigonometric Equations- 2 - Question 3

### The general solution of the equation tan2 a + 2 √3 tan a = 1 is given by

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 4

Total number of solutions of sin x . tan 4x = cos x belonging to (0, π) are

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 5

Cos²θ/2 =

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 6

If 2 tan2x – 5 sec x – 1 = 0 has 7 different roots in , n ∈ N, then greatest value of n is

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 7

The values of x between 0 and 2p which satisfy the equation sinx . = 1 are in A.P. The common difference of the A.P. is

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 8

Equation of the form P (sinx ± cosx, sinx cosx) = 0 where P(y, z) is a polynomial, can be solved by the change :

cos x ± sin x = t ; 1 ± 2 sin x cos x = t2. Reduce the given equation into P = 0

sin x + cos = 1 + sin x cos x is

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 9

If (cos x – sin x)  + 2 = 0, then x is

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 10

sin4x + cos4x = sin x cos x then x is–

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 11

The minimum value of 27cos2x 81sin2x is

Detailed Solution for JEE Advanced Level Test: Trigonometric Equations- 2 - Question 11

Let y = 27cos2x 81sin2x
= 3(3cos2x + 4sin2x)
- [32 + 42]1/2 ≤ 3cos2x + 4sin2x ≤ [32 + 42]1/2
= -5 ≤ 3cos2x + 4sin2x ≤ 5
3-5 ≤ 3cos2x + 4sin2x ≤ 35
= 1/243

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 12

Number of roots of the equation cos7 x + sin4 x = 1 in the interval [0, 2π] is

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 13

The smallest positive number of π for whcih the equation cos (π sin x) = sin (π cos x) has a solutionin [0, 2π] is

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 14

If sin θ + 7 cos θ = 5, then tan (θ/2) is a root of the equation

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 15

Match the following for number of solutions in [0, 2p]

Column - I Column - II

(A) sin2 q _ tan2 q = 1 (P) 2

(B) sin q + cos q = 1 (Q) 0

(C) tan q + sec q = 2cosq (R) 3

(D) 3sin2q _ 4 sinq + 1 = 0 (S) 1

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 16

What are the most general values of q which satisfy the equations,

(a) sin q =  (b) tan (x _ 1) =  (c) tanq = _1 (d) cosec q =

(e) 2cot2q = cosec2q

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 17

If 0 < t < 2π and sin t = - 1, then t =

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 18

Solve : cot q + tan q = 2 cosec q

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 19

Solve : sin2q = cos 3q

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 20

Solve : cot q = tan 8q

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 21

Solve : tan2q _ (1 + ) tan q +  = 0

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 22

Find all the angles between 0º and 90º which satisfy the equation sec2q . cosec2q + 2 cosec2q = 8

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 23

Solve : 4 cos q _ 3 sec q = 2 tan q

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 24

Solve : cot q _ tan q = 2

JEE Advanced Level Test: Trigonometric Equations- 2 - Question 25

Solve : sin q + sin 3q + sin 5q = 0