Test: Trigonometric Equations - JEE MCQ

# Test: Trigonometric Equations - JEE MCQ

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## 10 Questions MCQ Test - Test: Trigonometric Equations

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

### If sinθ = 1/2. How many solutions does this equation have between 0 and π ?

Detailed Solution for Test: Trigonometric Equations - Question 1

Two results are possible as π/6 & 5π/6 comes by subtracting π/6from π, In general we have Sin∆=nπ+(-1)^n(A) here A is π/6 and by putting different values of n in integer 2 values can be obtained

Test: Trigonometric Equations - Question 2

### The general solution of sin = 0 is

Detailed Solution for Test: Trigonometric Equations - Question 2

sinθ = 0
⇒ sin-1 θ = 0,π,2π,...
⇒ θ = 0 + nπ → n∈Z
The general solution for sin x = 0 will be, x = nπ, where n∈I.

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Test: Trigonometric Equations - Question 3

### if cosθ = √3/2. How many solutions does this equation have between -π and π ?

Detailed Solution for Test: Trigonometric Equations - Question 3

The general solution of the given question is theta= 2nπ± π/6 but it is mentioned that they are lies between -π to π. So when we put n=0 we get theta =±π/6. And when we put n= 1 we get theta does not lies between -π to ÷π. So we get only two values of theta.

Test: Trigonometric Equations - Question 4

The solution of cos 4x = cos 2x

Detailed Solution for Test: Trigonometric Equations - Question 4

cos 4x = cos 2x

Test: Trigonometric Equations - Question 5

The solution of sinθ cosθ = √3/4 is

Detailed Solution for Test: Trigonometric Equations - Question 5

Test: Trigonometric Equations - Question 6

The principal solution for tan x = √3 is,

Detailed Solution for Test: Trigonometric Equations - Question 6

Test: Trigonometric Equations - Question 7

The solution of the equation tan 2θ = tan θ/2 is

Detailed Solution for Test: Trigonometric Equations - Question 7

tanθ = tanα
θ = nπ + α
2θ = nπ + 2/θ
2(θ - 1/θ) = nπ
= θ - 1/θ = nπ/2
= θ2 - (nπθ)/2 - 1 = 0
θ = nπ/2 +- [(n2π2 + 4)1/2 ]/2
θ = nπ/2 +- [(n2 π2 + 16)1/2]/4

Test: Trigonometric Equations - Question 8

If tan x = tan α , then the general solution of the equation is

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Test: Trigonometric Equations - Question 9

tan(π + x)=

Detailed Solution for Test: Trigonometric Equations - Question 9

(180+theta ) lies in third quadrant...where tantheta is positive....tan(180+x)=tanx

Test: Trigonometric Equations - Question 10

The most general value that satisfies the equation cosecθ = 2 and cotθ = -√3 is

Detailed Solution for Test: Trigonometric Equations - Question 10

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