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/cosθ and cotθ =cosθ /sin θ
Trigonometric table:
Trigonometric Identities:
1. sin2θ + cos2θ = 1
2. 1 + tan2θ = sec2θ
3. 1 + cot2θ = cosec2θ
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
1. If 5tan θ = 4, then value of is : (5 sinθ-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 (tanθ/(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
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 + cot540 /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