# Trigonometry MCQ Mock Test Online Free

Trigonometry MCQs are different types of questions that come in all types of exams. Trigonometry plays an important role in Maths section. If you want to clear your concepts, then you can practice Mathematics introduction online from our website www.sarkarijobalert.com Trigonometry MCQ Test Free Mochak Test. This Introduction to Trigonometry Class 10 MCQs questions examines the understanding and concept of the chapter. You can test your knowledge and evaluate yourself. We suggest that you give as many online free MCQ mock tests as possible so that your concepts can be cleared.

## Trigonometry MCQ Online Free Mock Test 1

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Created on By Kamal Raj

Trigonometry Formulas

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If cos(α + β) = 0, then sin(α – β) can be reduced to

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The value of (sin 45° + cos 45°) is

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The value of (tan 1° tan 2° tan 3° … tan 89°) is

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The value of the expression [cosec (75° + θ) – sec (15° – θ) – tan (55° + θ) + cot (35° – θ)] is

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If ∆ABC is right angled at C, then the value of cos(A+B) is

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1 – cos2A is equal to:

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sin 2A = 2 sin A is true when A =

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2 tan 30°/(1 + tan230°) =

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The value of sin 60° cos 30° + sin 30° cos 60° is:

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(sin A – cos A)² is equal to _____

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If cos X = ⅔ then tan X is equal to:

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If sin A + sin2A = 1, then the value of the expression (cos2A + cos4A) is

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In a right triangle ABC, the right angle is at B. Which of the following is true about the other two angles A and C?

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(Sin 30°+cos 60°)-(sin 60° + cos 30°) is equal to:

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The value of tan 60°/cot 30° is equal to:

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In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. The value of tan C is:

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If cos a + 2cos b + cos c = 2 then a, b, c are in

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Evaluate sec² A + (1 + tan A) (1 – tan A).

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The value of tan 60°/cot 30° is equal to:

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If cos X = a/b, then sin X is equal to:

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## Example Trigonometry MCQ

1) Which of the following is the correct value of cot 100.cot 200.cot 600.cot 700.cot 800?

1. 1/√3
2. √3
3. -1
4. 1

Explanation: Here, we can apply the formula –

cot A. cot B = 1 (when A + B = 900)

= (cot 200 . cot 700) x (cot 100 . cot 800) x cot 600

= 1 x 1 x 1/√3

= 1/√3

So, the correct value of cot 100.cot 200.cot 600.cot 700.cot 800 = 1/√3

2) If tan θ + cot θ = 2, then what is the value of tan100 θ + cot100 θ?

1. 1
2. 3
3. 2
4. None of the above

Explanation: Given tan θ + cot θ = 2

Put θ = 450, above equation will satisfy as,

1 + 1 = 2

So, θ = 450,

= tan100 450 + cot100 450

= 1100 + 1100

= 2

3) If x and y are complementary angles, then
(a) sin x = sin y
(b) tan x = tan y
(c) cos x = cos y
(d) sec x = cosec y

4) If A and (2A – 45°) are acute angles such that sin A = cos (2A – 45°), then tan A is equal to

A. 0
B. 1/√3
C. 1
D. √3

5) If θ is said to be an acute angle, and 7 sin2 θ + 3 cos2 θ = 4, then what is the value of tan θ?

1. 1
2. √3
3. 1/√3
4. None of the above

Explanation: Given 7 sin2 θ + 3 cos2 θ = 4

=> 7 sin2 θ + 3 (1 – sin2 θ) = 4

=> 7 sin2 θ + 3 – 3sin2 θ = 4

Then, 4sin2 θ = 1

Or, sin θ = 1/2

So, θ = 300

Now, put θ = 300 in tan θ, we will get,

tan θ = 1/√3

6) Suppose cos θ + sin θ = √2 cos θ, then which of the following is the correct value of cos θ – sin θ?

1. √2 cos θ
2. √2 sin θ
3. -√2 cos θ
4. -√2 sin θ

Explanation: It is given that, cos θ + sin θ = √2 cos θ …..(i)

On squaring both sides, we will get,

(cos θ + sin θ)2 = (√2 cos θ)2

=> cos2 θ + sin2 θ + 2 sin θ cos θ = 2 cos2 θ

Or, 2cos2 θ – cos2 θ – sin2 θ = 2 sinθ cosθ

=> cos2 θ – sin2 θ = 2 sin θ cos θ

=> (cos θ + sin θ) (cos θ – sin θ) = 2 sin θ cos θ

=> (√2 cos θ) (cos θ – sin θ) = 2 sin θ cos θ [from equation (i)]

=> (cos θ – sin θ) = 2 sinθ cosθ / √2 cos θ

= √2 sin θ

7) The value of cos 180° is
(a) 0
(b) 1
(c) -1
(d) infinite

Hint:
180 is a standard degree generally we all know their values but if we want to go theoretically then
cos(90 + x) = – sin(x)
So, cos 180 = cos(90 + 90)
= -sin 90
= -1 {sin 90 = 1}
So, cos 180 = -1

8) In given figure, the length of AP is

Explaination:

9) If the value of tanP + secP = a, then what is the value of cosP?

1. 2a/a2 + 1
2. a2 + 1/ 2a
3. a2 – 1/ 2a
4. None of the above

Explanation: It is given that, tanP + secP = a ……(i)

As we know, the trigonometric identity, sec2 P – tan2 P = 1 {we assume θ = P}

So, we can apply the formula a2 – b2 = (a – b) (a + b)

=> (sec P – tan P) (sec P + tan P) = 1

=> (sec P – tan P) x a = 1

=> sec P – tan P = 1/a …..(ii)

So, from equation (i) and (ii), we will get –

2sec P = a + 1/a

sec P = a2+1 / 2a

So, cos P = 2a / a2+1 [as sec P = 1/cosP]

10) Which of the following is the correct value of (3 / 1+tan2 θ) + 2 sin2 θ + (1 / 1+cot2 θ)?

1. 3
2. 9
3. 6
4. None of the above

Explanation: (3 / 1+tan2 θ) + 2 sin2 θ + (1 / 1+cot2 θ) = ?

According to the trigonometric identities, the given equation can be written as –

= 3/sec2 θ + 2 sin2 θ + 1/cosec2 θ

= 3cos2 θ + 2 sin2 θ + sin2 θ

= 3cos2 θ + 3sin2 θ

= 3(cos2 θ + sin2 θ)

= 3