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I've got this sample paper from somewhere and solved it fully, I am requesting to anyone, if he/she can get me these solutions,

I don't remember from where I'd downloaded it sadly. I'ld be greatful if someone would post the solutions, from google maybe.

SAMPLE PAPER- INTRODUCTION TO TRIGONOMETRY

CLASS-X CBSE

  1. If tanθ=1, find the value of sin4θ +cos4θ.
  2. sin(45 – θ) – cos(45 + θ) =?
  3. If 3 tanθ=4,find 3 sinθ – cosθ

3 sinθ + cosθ

  1. Find the value of sin2200 + sin2700 + sin2650 +cos650 sin250

cos2200 + cos2700

  1. If sinα=1/2 and cosβ=1/2, find the value of α + β.
  2. If cos A + cos2A=1, then find the value of sin2A + sin4A.
  3. If sin9α=cosα and 9α<900, find cot5α.
  4. Find the value of tan10 tan20 tan30 …….tan890.
  5. If sin (α + β) =1, then cos (α – β) =?
  6. Find the value of cosec (700 + θ) – sec (200 – θ) – tan (500 + θ) + cot (400 – θ).

  1. If sinB=1/2, then find the value of 4cos3B-3cosB.
  2. If secθ=2, then find the value of tan2θ – sin2θ.
  3. If tanA=1/√3 and tanB=√3, then prove that tan(A+B) = tanA + tanB

1- tanAtanB

  1. Prove that sin2θ + cos2θ = 1.
  2. Prove that sec2θ – tan2θ =1.
  3. Prove that cosec2θ – cot2θ =1.
  4. Express sinθ in terms of all other trigonometric ratios.
  5. Express cosθ in terms of all other trigonometric ratios.
  6. Express tanθ in terms of all other trigonometric ratios.
  7. Express cosecθ in terms of all other trigonometric ratios.

  1. Evaluate: (2/3)cosec2580 – (2/3)cot580 tan 320 – (5/3)tan130 tan 370 tan 450 tan 530 tan 770.
  2. If cotθ = 15/8, then evaluate (2 + 2sinθ) (1 – sinθ)

(1 + cosθ) (2 – 2cosθ)

  1. Without using trigonometric tables, Evaluate:

Cos580 + sin220 - cos380 cosec520

Sin320 cos680 tan180 tan350 tan600 tan720 tan550

  1. If sinθ = 1/3, then find the value of (2cot2θ + 2).
  2. If A, B and C are the interior angles of a triangle ABC, then show that tan (B + C) = cot A

2 2

  1. If sec (A + B) =2 and sec (A – B) = 2/√3; 00<A + B ≤900; A>B Find A and B.
  2. In ∆ ABC, Right angled at B, If tanA=√3, find the value of:

(i) sinA cosC + cosA sinC.

(ii) cosA cosC + sinA sinC.

  1. If sec P=cosec Q, Prove that P+Q=900.
  2. If sec2A(1 + sin A) (1- sinA) =K, Find the value of K.
  3. If 3 cot A=4, check whether tan2A – sin2A = sin2A tan2A or not.
  1. Prove that sec2θ +cosec2θ = sec2θ cosec2θ.
  2. Prove that 1 + cosθ – sin2θ =cotθ

sinθ(1 + cosθ)

  1. tanθ + cotθ = 1 + tanθ + cotθ

1-cotθ 1-tanθ

  1. Prove that (1 + cotA – cosecA) (1 + tanA + secA) =2.
  2. Prove that (1 + cotA + tanA) (sinA – cosA) = sinA tan A – cotA cosA.
  3. Simplify sin3A +cos3A + sinA cosA

sinA + cosA

  1. Prove that (cosecθ – sinθ) (secθ – cosθ) = ______1______

tanθ + cotθ

  1. Prove that : secθ + tanθ – 1 = 1+sinθ

secθ - tanθ + 1 cosθ

  1. Prove that: (tanA – tanB)2 + (1 + tanAtanB)2 =sec2A sec2B.
  2. Prove that : cosA + sinA = sinA + cosA

1-tanA 1-cotA

41. If xcosA – ysinA = a, xsinA+ ycos A = b, prove that x2+y2=a2+b2

42. S.T Sec2 θ + Cosec2 θ can never be less than 2.

43. If sin θ = 1/2 , show that 3cos θ - 4cos3 θ = 0.

44. If 7sin2 θ + 3cos2 θ = 4, show that tan θ = 1/√3.

45. If cos θ +sin θ = √2 cos θ, prove that cos θ – sin θ =√2 sin θ.

46. If tanA+sinA=m and tanA-sinA=n, show that m2-n2 = 4.

47. If secA= x+, prove that secA+tanA=2x or

48. Solve for θ, if tan5 θ = 1.

49. If 7 cosec θ -3cot θ = 7, prove that 7cot θ - 3cosec θ = 3.

50. If Sec θ +Tan θ =4 find sin θ , cos θ.

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