Important Question (1 Mark): Introduction to Trigonometry - Class 10 MCQ

# Important Question (1 Mark): Introduction to Trigonometry - Class 10 MCQ

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## 25 Questions MCQ Test Online MCQ Tests for Class 10 - Important Question (1 Mark): Introduction to Trigonometry

Important Question (1 Mark): Introduction to Trigonometry for Class 10 2024 is part of Online MCQ Tests for Class 10 preparation. The Important Question (1 Mark): Introduction to Trigonometry questions and answers have been prepared according to the Class 10 exam syllabus.The Important Question (1 Mark): Introduction to Trigonometry MCQs are made for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Important Question (1 Mark): Introduction to Trigonometry below.
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Important Question (1 Mark): Introduction to Trigonometry - Question 1

### If sin θ = 5/13 then cos θ =

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Important Question (1 Mark): Introduction to Trigonometry - Question 2

### Which of the following is true:

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Trigonometric ratio  is correct.

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Important Question (1 Mark): Introduction to Trigonometry - Question 3

### If √3tanθ = 3sinθ, then the value of sin2θ−cos2θ is

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Important Question (1 Mark): Introduction to Trigonometry - Question 4

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Important Question (1 Mark): Introduction to Trigonometry - Question 5

If sec A + tan A = m and sec A – tan A = n, then the value of mn is

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Important Question (1 Mark): Introduction to Trigonometry - Question 6

If 4tan θ = 3,

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Important Question (1 Mark): Introduction to Trigonometry - Question 7

cot A tan A =

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Important Question (1 Mark): Introduction to Trigonometry - Question 8

If sin θ − cos θ = 0, vthen the value of θ is

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Important Question (1 Mark): Introduction to Trigonometry - Question 9

If tan θ = √3, the sec θ =

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Important Question (1 Mark): Introduction to Trigonometry - Question 10

Given that sin A=1/2 and cos B=1/√2 then the value of (A + B) is:

Important Question (1 Mark): Introduction to Trigonometry - Question 11

If cot θ = 7/8, then the value of (1 + sin θ)(1 - sin θ) / (1 + cos θ)(1 - cos θ)

Detailed Solution for Important Question (1 Mark): Introduction to Trigonometry - Question 11

We will use the basic concepts of trigonometric ratios to solve the problem.

Consider ΔABC as shown below where angle B is a right angle.

cot θ = side adjacent to θ / side opposite to θ = AB/BC = 7/8

Let AB = 7k and BC = 8k, where k is a positive integer.

By applying Pythagoras theorem in Δ ABC, we get

AC2 = AB2 + BC2

= (7k)+ (8k)2

= 49k2 + 64k2

= 113k2

AC = √113k2

= √113k

Therefore, sin θ = side opposite to θ / hypotenuse = BC/AC = 8k/√113k = 8/√113

cos θ = side adjacent to θ / hypotenuse = AB/AC = 7k/√113k = 7/√113

(i) (1 + sin θ) (1 - sin θ) / (1 + cos θ) (1 - cos θ) = 1 - sin2θ / 1 - cos2θ  [Since, (a + b)(a - b) = (a2 - b2)]

= [1 - (8/√113)2] / [1 - (7/√113)2]

= (1 - 64/113) / (1 - 49/113)

= (49/113) / (64/113)

= 49/64

Important Question (1 Mark): Introduction to Trigonometry - Question 12

Given that sinθ = a/b then cos θ is equal to

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Important Question (1 Mark): Introduction to Trigonometry - Question 13

The value of

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Important Question (1 Mark): Introduction to Trigonometry - Question 14

If (α + β) = 90°, then the value of

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Important Question (1 Mark): Introduction to Trigonometry - Question 15

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Important Question (1 Mark): Introduction to Trigonometry - Question 16

In right triangle ABC, right angled at C, if tan A = 1, then the value of 2 sin A cos A is

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Important Question (1 Mark): Introduction to Trigonometry - Question 17

The value of sin60cos30∘ + sin30cos60 is

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Important Question (1 Mark): Introduction to Trigonometry - Question 18

If sin θ − cos θ = 0, then the value of sin4θ + cos4θ is

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Important Question (1 Mark): Introduction to Trigonometry - Question 19

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Important Question (1 Mark): Introduction to Trigonometry - Question 20

If x = a cos θ and y = b sin θ, then the value of b2x+ a2y2 is

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Important Question (1 Mark): Introduction to Trigonometry - Question 21

If tan θ = 20/21, then

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Important Question (1 Mark): Introduction to Trigonometry - Question 22

The value of 2 tan245+ cos230∘ − sin260 is

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Important Question (1 Mark): Introduction to Trigonometry - Question 23

The value of tan 1 tan 2∘ tan 3………… tan 89 is

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tan 1° tan2° tan3° ..............tan 89°
= tan(90° -  89°) tan(90° - 88°) tan(90° -  87°) .........  tan 87° tan 88° tan 89°
= cot 89° cot 88° cot 87° .............tan 87° tan 88° tan 89°
= (cot 89° tan 89°) (cot 88° tan 88°) (cot 87° tan 87°) .............(cot 44° tan 44°) tan 45°
= 1x1x1x1x1.........1 = 1

Important Question (1 Mark): Introduction to Trigonometry - Question 24

(sec2θ - 1) (1 - cosec2θ) =

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Important Question (1 Mark): Introduction to Trigonometry - Question 25

If x = a sec θ cos φ, y = b sec θ sin φ and z = c tan θ, then the value of

Detailed Solution for Important Question (1 Mark): Introduction to Trigonometry - Question 25

Given: x = a sec θ cos φ, y = b sec θ sin φ and z = c tan θ

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