Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Mathematics (Maths) Class 10

Class 10 : Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

The document Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.
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Q16. For an acute angle θ , show that: (sin θ − cosec θ) (cos θ − sec θ) Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Q20. Without using trigonometric tables evaluate:
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Q21. If tan (A + B) = √3 and tan (A − B) = 1, 0° < A + B < 90°; A > B, then find A and B.

Sol. We have: tan (A + B) = 3 (Given)
tan 60° = 3 (From the table)
⇒ A + B = 60° ...(1)
Also,tan (A − B)= 1 [Given]
and cosec 60° = 2 and cos 90° = 0
⇒ A − B = 45 ...(2)
Adding (1) and (2),
2A = 60° + 45° = 105°

⇒ Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

From (2), 52.5° − B = 45°
⇒ B = 52.5° − 45° = 7.5°
Thus, A = 52.5° and B = 7.5°.

Q22. If tan (2A) = cot (A − 21°), where 2A is an acute angle, then find the value of A.

Sol. We have: tan (2A) = cot (A − 21°)
∵ cot (90°− θ) = tan θ
∴ cot (90°− 2A) = tan 2A
⇒ cot (90°− 2A) = cot (A − 21)°
⇒ 90 − 2A = A − 21°
⇒ − 2A − A = − 21°− 90°
⇒ − 3A = − 111°

⇒  Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Q23. If sin 3A = cos (A − 10°), then find the value of A, where 3A is an acute angle.

Sol. We have:
sin 3A = cos (A − 10°)
∵ cos (90° − θ) = sin θ
∴ cos (90° − 3A) = sin 3A
⇒ 90° − 3A = A − 10°
⇒ −3A − A = −10° − 90°
⇒ −4A = −100°

⇒ Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Q24. If sec 2A = cosec (A − 27°), then find the value of A, where 2A is an acute angle.

Sol. We have:

sec 2A = cosec (A − 27°) ...(1)
∵ sec θ = cosec (90° − θ)
∴ sec 2A = cosec (90° − 2A) ...(2)

From (1) and (2), we get
A − 27° = 90° − 2A
⇒ A + 2A = 90 + 27° = 117°
⇒ 3A = 117°
⇒  Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Q25. Simplify:

Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev + sin θ cos θ

Sol. We have:

Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRevShort Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

= 1 = R.H.S.

Q28. Without using trigonometrical tables, evaluate:

Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Sol.

Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRevShort Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

[∵ sin (90° − θ) = cos θ, cos (90° − θ) = sin θ, cosec (90° − θ) = sec θ, and tan (90° − θ) = cot θ]
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Q29. Using Geometry, find the value of sin 60°.

Sol. Let us consider an equilateral ΔABC and draw AD ⊥ BC.
Since, each angle of an equilateral triangle = 60°
∴∠A = ∠B = ∠C = 60°

Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Let AB = BC = AC = 2a

In ΔABD and ΔACD, we have:
AB = AC   [Given]
∠ADB = ∠ADC = 90°    [Construction]
AD = AD [Construction]
⇒ ΔABD ≅ ΔACD
⇒ BD = CD

Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Now, using Pythagoras theorem, in right ΔABD,

AD2 = AB2 − BD2
= (2a)2 − a2
= 4a2 − a2
= 3a2

⇒ Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

∴  Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

Thus,  Short Answer Type Questions(Part- 2)- Introduction to Trigonometry Class 10 Notes | EduRev

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