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 Entrancei. 

SUMMARY

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

Trigonometric table:

Trigonometric Identities:

1. sin²θ + cos²θ = 1

2. 1 + tan²θ = sec²θ

3. 1 + cot²θ = cosec²θ

Trigonometric ratios of complementary angles:

Sin (90⁰- θ) = cos θ

cos (90⁰- θ) = sin θ

Tan (90⁰- θ) = cot θ

Cot (90⁰- θ) = tan θ

Sec (90⁰- θ) = cosec θ

Cosec (90⁰- θ) = sec θ

OBJECTIVE

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

a) 1/3

b)1/6

c)4/5

d)2/3

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

a) 9

b)9/5

c)1/3

d)1/9

3. If tan θ= 4, then (tan⁡θ/(sin³ θ)/cosθ+sinθcosθ))is equal to:

a) 0

b)2√2

c)√2

d)1

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

a) Increases

b) decreases

c) remains constant

d) increases, then decreases

5. Value of x from the equation

x sin⁡ π/6 cos² π/4 = (cot² π/6 sec π/3 tan π/4)/(cosec² π/4 cosec π/6) is :

a) 4

b) 6

c) -2

d) 0

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

a) cos-¹(1/3)

b) cos-¹(1/6)

c) cos-¹(1/6)

d)Sin-¹(1/3)

7. If α + β = 90⁰ and α = 2β, then cos² + sin²β equals to:

a) 1/2

b) 0

c) 1

d) 2

SUBJECTIVE

1. If A + B = 90⁰, prove that:

√(tanAtanB+tanAcotB)/sinAsecB-(sin² B)/(cos² A)=tanA

Prove the following (Q 2 to Q5)

2. tanθ/(1-cotθ) +cotθ/(1-tanθ) = secθcosecθ+1

3. (sinA+cosA)/(sinA-cosA)+ (sinA-cosA)/(sinA+cosA)= 2/(sin² A-cos² A)=2/(1-2cos² A)

4. ( sin⁸θ-cos⁸θ) = (sin²θ-cos²θ)(1-sin² θcos² 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: x²+y²+z²=r².

7. Prove that:

1/(secx-tanx)-1/cosx=1/cosx-1/(secx+tanx)

8. Evaluate: tan 7⁰ tan 23⁰ tan 60⁰ tan 67⁰ tan 83⁰ + cot⁡54⁰ /tan 36⁰ + sin 20⁰ sec 70⁰- 2

9. Evaluate: cosec²58⁰ - cot 58⁰tan 32⁰ - tan 13⁰ tan 37⁰ tan 45⁰ tan 53⁰ tan 77⁰.

10. If 5x = sec θ and = tanθ, find the value of 5 (x²-1/x² ).

11. Find the value of sec 60⁰ geometrically.

12. Prove the following: sin A(1 + tan A) + cos A(1 + cot A) = sec A + cosec A.

Answers:

Objective:

1) b

2) a

3) d

4) b

5) b

6) d

7) a

Subjective:

8) √3

9)-1

10)

11) 2