Previous Year Questions: Introduction to Trigonometry

# Class 10 Maths Chapter 8 Previous Year Questions - Introduction to Trigonometry

 Table of contents Previous Year Questions 2024 Previous Year Questions 2023 Previous Year Questions 2022 Previous Year Questions 2021 Previous Year Questions 2020 Previous Year Questions 2019

## Previous Year Questions 2024

Q1: If sin α = √3/2 , cos β = √3/2 then tan α. tan β is:     (2024)
(a) √3
(b) 1/√3
(c) 1
(d) 0

Ans: (c)

Q2: Evaluate:         (2024)

Ans:

Q3: Prove that: (cosec θ – sin θ) (sec θ – cos θ) (tan θ + cot θ) = 1     (2024)

Ans:
L.H.S. = (cosec θ – sin θ) (sec θ – cos θ) (tan θ + cot θ)
= (cosec θ – sin θ) (sec θ – cos θ) (tan θ + cot θ)

= 1 = R.H.S.
Hence, proved.

## Previous Year Questions 2023

Q4: If 2 tan A = 3, then find the value of  is  (2023)

Ans:

Q5: [5/8 sec260° - tan260° + cos245° is equal to    (2023)
(a) 5/3
(b) -1/2
(c) 0
(d) -1/4

Ans: (c)
Sol:

Q6: Evaluate 2 sec2θ + 3 cosec2θ - 2 sin θ cos θ if θ = 45°  (2023)

Ans: Since θ = 45°, sec 45° = √2, cosec 45° = √2, sin 45° = 1/√2 cos 45° = 1/√2
2sec2 θ + 3 cosec2 θ – 2 sin θ cos θ

= 4 + 6 – 1 = 9

Q7: Which of the following is true for all values of θ(0o ≤ θ ≤ 90o)?  (2023)
(a)
cos2θ - sin2θ - 1
(b)
cosec2θ - sec2θ- 1
(c)
sec2θ - tan2θ - 1
(d)
cot2θ- tan2θ = 1

Ans: (c)

Q8: If sinθ +cosθ = √3. then find the value of sinθ . cosθ.  (2023)

Ans: Given, sinθ +cosθ = √3
Squaring both sides, we get (sinθ + corsθ)2 = 3
⇒ sin2θ + cos2θ + 2sinθ cosθ = 3
⇒ 2sinθ cosθ = 3 - 1     ( ∵ sin2θ + cos2θ = 1)
⇒ 2sinθ cosθ = 2
⇒  sinθ cosθ = 1

Q9: If  sin α = 1/√2 and cot β = √3, then find the value of cosec α + cosec β.  (2023)

Ans: Given, sin α = 1/√2 and cot β = √3
We know that, cosec α = 1/sinα = √2
Also, 1 + cot2β = cosec2β
⇒ cosec2β = 4
⇒ cosec β = 4
Now, cosec α + cosec β = √2 + 2

Q10: Prove that the Following Identities: Sec A (1 + Sin A) ( Sec A - tan A) = 1  (2023)

Ans: LHS = sec A(1 + sin A )( sec A - tan A)

= 1
= RHS
Hence proved..

## Previous Year Questions 2022

Q11: Given that cos θ = √3/2, then the value of   is  (2022)
(a) -1
(b) 1
(c) 1/2
(d) -1/2

Ans: (c)
Sol:
Given, cosθ = √3/2  = B/H

Let B = √3k and H = 2k
[By Pythagoras Theorem]
⇒√k2 = k

Q12:  is equal to   (2022)
(a) 0
(b) 1
(c) sinθ + cosθ
(d) sinθ - cosθ

Ans: (c)
Sol: We have,

Q13: The value of θ for which 2 sin2θ = 1, is   (2022)
(a) 15°
(b) 30°
(c) 45°
(d) 60°

Ans: (a)
Sol: Given, 2 sin2θ = 1 ⇒ sin2θ = 1/2
⇒ 2θ = 30°
⇒ θ = 15°

Q14: If sin2θ + sinθ = 1, then find the value of cos2θ + cos4θ is   (2022)
(a) -1
(b) 1
(c) 0
(d) 2

Ans: (b)
Sol: Given, sin2θ + sinθ = 1   ---(i)
sinθ = 1 - sin2θ
⇒ sinθ = cos2θ  ---(ii)
∴ cos2θ + cos4θ
= sinθ + sin2θ       [From (ii)]
= 1        [From (i)]

## Previous Year Questions 2021

Q15: If 3 sin A = 1. then find the value of sec A.    (2021 C)

Ans: We have, 3 sin A = 1
∴ sin A = 1/3
Now by using cosA = 1 - sin2 A, we get

Q16: Show that:     (2021 C)

Ans: We have, L.H.S.

[By using 1 + tan2θ = sec2θ and 1 + cot2 θ = cosec2θ ]

Hence,

## Previous Year Questions 2020

Q17: If sin θ = cos θ, then the value of tan2 θ + cot2 θ is    (2020)
(a) 2
(b) 4
(c) 1
(d) 10/3

Ans: (a)
Sol: We have, sin θ = cos θ
or sin θ / cos θ = 1
⇒ tan θ = 1 and cot θ = 1     [∵ cot θ = 1/tanθ]
∴ tanθ + cotθ = 1 + 1 = 2
Hence, A option is correct.

Q18: Given 15 cot A = 8, then find the values of sin A and sec A.    (2020)

Ans: In right angle ΔABC we have
15 cot A = 8
⇒ cot A = 8/15

Since, cot A = AB/BC
∴ AB/BC = 8/15
Let AB = 8k and BC = 15k
By using Pythagoras theorem, we get
AC= AB2 + BC2
⇒ (8k)2 + (15)2 = 64k2 + 225k2 = 289k2 = (17k)

So, sec A = 1/cosA = 17/8

Q19: Write the value of sin2 30° + cos2 60°.     (2020)

Ans:  We have, sin2 30° + cos2 60°

Q20: The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ − b cos θ) is      (2020)
(a) a+ b2
(b) a + b
(c)
(d)

Ans: (c)
Sol: Given the point A (cos θ + b sin θ , 0), (0 , a sin θ − b cos θ)
By distance formula,
The distance of

[∵ cos2θ + sin2θ = 1]

Q21: 5 tan2θ - 5 sec2θ = ____________.    (2020)

Ans: We have 5(tan2θ - sec2θ)
= 5(-1) = - 5 [By using 1 + tan2θ = sec2 θ ⇒ tan2θ - sec2θ = - 1]

Q22: If sinθ + cosθ = √3. then prove that tan θ + cot θ = 1    (2020)

Ans: sin θ + cos θ =√3
= (sinθ + cosθ)= 3
= sin2 θ + cos2 θ + 2sin θ cos θ = 3
⇒ 2sin θ cos θ = 2
⇒ sin θ cos θ = 1
⇒ sin θ cos θ = sin2θ + cos2θ

⇒ tan θ + cot θ = 1

## Previous Year Questions 2019

Q23: If sin x + cos y = 1, x = 30° and y is acute angle, find the value of y.    (2019)

Ans: Given,
⇒ sin x + cos y = 1
⇒ sin 30° + cos y = 1
⇒ 1/2 + cos y = 1
⇒ cos y = 1 - 1/2
⇒ cos y = 1/2
⇒ cos y = cos 60°.
Hence, y = 60°.

Q24: If cosec2 θ (cos θ - 1)(1 + cos θ) = k, then what is the value of k?   (2019)

Ans:  Given:
cosec2 θ (cos θ - 1)(1 + cos θ) = k
Concept used:
Cosec α = 1/Sin α
Sin2 α + Cos2 α = 1
(a + b)(a - b) = a2 - b2
Calculation:
cosec2 θ (cos θ - 1)(1 + cos θ) = k
⇒ cosec2 θ (1 - cos θ)(1 + cos θ) = -k
⇒ cosec2 θ (1 - cos2 θ) = -k
⇒ cosec2 θ × sin2 θ = -k
⇒ 1 = -k
⇒ k = -1
∴ The value of k is (-1).

Q25: The value of ( 1 + cot A − cosec A ) ( 1 + tan A + sec A ) is

Ans:

The document Class 10 Maths Chapter 8 Previous Year Questions - Introduction to Trigonometry is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10

## Mathematics (Maths) Class 10

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## FAQs on Class 10 Maths Chapter 8 Previous Year Questions - Introduction to Trigonometry

 1. What are the basic trigonometric ratios?
Ans. The basic trigonometric ratios in a right triangle are sine (sin), cosine (cos), and tangent (tan), which are defined as the ratios of the lengths of the sides of a right triangle.
 2. How do you find the sine, cosine, and tangent of an angle in a right triangle?
Ans. To find the sine, cosine, and tangent of an angle in a right triangle, you can use the following formulas: - Sin(angle) = Opposite/Hypotenuse - Cos(angle) = Adjacent/Hypotenuse - Tan(angle) = Opposite/Adjacent
 3. What is the Pythagorean trigonometric identity?
Ans. The Pythagorean trigonometric identity states that for any angle in a right triangle, the sum of the squares of the sine and cosine of that angle is always equal to 1. This identity is represented as sin^2(angle) + cos^2(angle) = 1.
 4. How do you solve trigonometric equations?
Ans. To solve trigonometric equations, you can use algebraic manipulation and trigonometric identities to simplify the equation and find the value of the unknown angle or variable.
 5. How is trigonometry used in real-life applications?
Ans. Trigonometry is used in various real-life applications such as architecture, engineering, physics, and navigation to calculate distances, angles, heights, and other measurements using the principles of triangles and trigonometric functions.

## Mathematics (Maths) Class 10

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