Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Mathematics (Maths) Class 10

Class 10 : Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

The document Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.
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Q1. It is given that tan (θ1 + θ2) =  Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev where θ1 and θ2 areacute angles. Calculate θ1 + θ2 when tan θ1Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Now,tan (θ1 + θ2) = 1 ⇒ θ1 + θ2 = 45°.

Q2. Prove that:   Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Q3. Prove that:  (sin4 θ – cos4 θ +1) cosec2 θ = 2  

Sol. L.H.S.

= (sin4 θ – cos4 θ + 1) cosec2 θ
= [(sin2 θ)2 – (cos2 θ)2 + (sin2 θ + cos2θ)] cosec2 θ [∵ sin2 θ + cos2 θ = 1]
= [(sin2 θ – cos2 θ) (sin2 θ + cos2 θ) + (sin2θ + cos2 θ)] cosec2 θ
= [(sin2 θ – cos2 θ) 1 + 1] cosec2 θ
= (sin2 θ – cos2 θ) + cosec2 θ
= [(sin2 θ + (1 –cos2 θ)] cosec2 θ
= [sin2 θ + sin2 θ] cosec2 θ   [∵ 1 – cos2 θ = sin2 θ]
= 2 sin2 θ . cosec2 θ
= 2 = RHS [∵ sin θ . cosec θ = 1]

Q4. Prove that: sec2 θ + cosec2 θ = sec2 θ · cosec2 θ 

Sol. L.H.S. = sec2 θ + cosec2 θ

Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRevShort Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Q6. Given that α + β = 90°, show that:  Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Sol. ∵ α + β =90°
∵ β = (90 – a)
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Q10. Prove that: sin6θ + cos6θ + 3sin2θ cos2θ = 1.

Sol. ∵ sin2 θ + cos2θ = 1
∵ (sin2 θ + cos2 θ)3 = (1)3 = 1
⇒ (sin2 θ) 3 + (cos2 θ)3 + 3 sin2 θ . cos2 θ (sin2 θ + cos2 θ) = 1
⇒ sin6 θ + cos6 θ + 3 sin2 θ . cos2θ (1) = 1
⇒ sin6 θ + cos6 θ + 3 sin2 θ . cos2 θ = 1

Q11. Prove that: a2 + b2 = x2 + y2 when a cos θ − b sin θ = x and a sin θ + b cos θ = y.

Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev = 2 cosec A

Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev
Short Answer Type Questions(Part- 1)- Introduction to Trigonometry Class 10 Notes | EduRev

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