CBSE Worksheet for chapter- 9 Trigonometry class 10

CBSE Worksheet for chapter- 9 Trigonometry class 10

Worksheet For class 10

Find CBSE Worksheet for chapter- 9 Trigonometry class 10

CLASS-10

BOARD: CBSE

Mathematic Worksheet - 9

TOPIC: Trigonometry

For other CBSE Worksheet for class 10 Mathematic check out main page of Physics Wallah.

SUMMARY

tan θ= sin θ/cos⁡θ and cotθ =cos⁡θ /sin θ

Trigonometric table:

Trigonometric Identities:

1. sin ² θ + cos ² θ = 1
2. 1 + tan ² θ = sec ² θ
3. 1 + cot ² θ = cosec ² θ

Trigonometric ratios of complementary angles:

• Sin (90 ⁰ - θ) = cos θ
• cos (90 ⁰ - θ) = sin θ
• Tan (90 ⁰ - θ) = cot θ
• Cot (90 ⁰ - θ) = tan θ
• Sec (90 ⁰ - θ) = cosec θ
• Cosec (90 ⁰ - θ) = sec θ

OBJECTIVE

1. If 5tan θ = 4, then value of is : (5 sin⁡θ-3 cosθ)/(5 sinθ+3 cosθ)

1. 1/3
2. 1/6
3. 4/5
4. 2/3

2. Given 3sin β + 5cos β = 5, then the value of (3cos β- 5sin β) ² is equal to:

1. 9
2. 9/5
3. 1/3
4. 1/9

3. If tan θ= 4, then (tan⁡θ/(sin ³ θ)/cosθ+sinθcosθ))is equal to:

1. 0
2. 2√2
3. √2
4. 1

4. As x increases from 0 to π/2 , the value of cos x :

1. Increases
2. decreases
3. remains constant
4. increases, then decreases

5. Value of x from the equation

x sin⁡ π/6 cos ² π/4 = (cot ² π/6 sec π/3 tan π/4)/(cosec ² π/4 cosec π/6) is :

1. 4
2. 6
3. -2
4. 0

6. The area of a triangle is 12 sq. cm. Two sides are 6 cm and 12 cm. The included angle is :

1. cos- ¹ (1/3)
2. cos- ¹ (1/6)
3. cos- ¹ (1/6)
4. Sin- ¹ (1/3)

7. If α + β = 90 ⁰ and α = 2β, then cos ² + sin ² β equals to:

1. 1/2
2. 0
3. 1
4. 2

SUBJECTIVE

1. If A + B = 90 ⁰ , prove that:
   √(tanAtanB+tanAcotB)/sinAsecB-(sin ² B)/(cos ² A)=tanA
2. tanθ/(1-cotθ) +cotθ/(1-tanθ) = secθcosecθ+1
3. (sinA+cosA)/(sinA-cosA)+ (sinA-cosA)/(sinA+cosA)= 2/(sin ² A-cos ² A)=2/(1-2cos ² A)
4. ( sin ⁸ θ-cos ⁸ θ) = (sin ² θ-cos ² θ)(1-sin ² θcos ² θ)
5. (tanθ+secθ-1)/(tanθ-secθ+1) =(1+sinθ)/cosθ
6. If x = r sin θ cos φ, y = r sin θ sin φ, z = r cos θ, then prove that: x ² +y ² +z ² =r ² .
7. Prove that:
   1/(secx-tanx)-1/cosx=1/cosx-1/(secx+tanx)
8. Evaluate: tan 7 ⁰ tan 23 ⁰ tan 60 ⁰ tan 67 ⁰ tan 83 ⁰ + cot⁡54 ⁰ /tan 36 ⁰ + sin 20 ⁰ sec 70 ⁰ - 2
9. Evaluate: cosec ² 58 ⁰ - cot 58 ⁰ tan 32 ⁰ - tan 13 ⁰ tan 37 ⁰ tan 45 ⁰ tan 53 ⁰ tan 77 ⁰ .
10. If 5x = sec θ and = tanθ, find the value of 5 (x ² -1/x ² ).
11. Find the value of sec 60 ⁰ geometrically.
12. Prove the following: sin A(1 + tan A) + cos A(1 + cot A) = sec A + cosec A

Prove the following (Q 2 to Q5)

Answers:

Objective:

1. b
2. a
3. d
4. b
5. b
6. d
7. a

Subjective:

8. √3
9. -1
10. 2