Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev

Mathematics (Maths) Class 10

Class 10 : Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev

The document Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev is a part of the Class 10 Course Mathematics (Maths) Class 10.
All you need of Class 10 at this link: Class 10

Short Answer Type Questions

Q 1. Find the value of (sin233° + sin257°)     [Delhi 2019]
Ans: sin233° + sin257°
⇒ sin233° + sin2( 90° - 33°)
⇒ sin233° + cos233   [Using sin(90° - θ) = cos θ]
⇒ 1    [Using sin2θ + cos2 θ = 1]

Q 2. sin2 60° + 2 tan 45° - cos2 30°    [Allahabad 2019] 
Ans:  2
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev

Q 3. Evaluate:         [CBSE 2019 (30/5/1)]
(i) Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev
(ii) cos 48° - sin 42
°
Ans:
(i)  Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev
(ii) cos 48° - sin 42° = cos (90° - 42°) - sin 42°
= sin 42° - sin 42° = 0

Q 4. If sin x + cos y = 1; x = 30° andy is an acute angle, find the value of y.    

[CBSE 2019 (30/5/1)]
Ans: 
We have, sin x + cosy = 1
⇒ sin30° + cosy = 1
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev
⇒ y = 600

Q 5. Prove that: (1 + cot A - cosec A)(l + tan A + sec A) = 2   [CBSE 2019 (30/1/2)]
Ans:
LHS = (1 + cotA-cosecA) (1 + tanA +secA)
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev

Q 6. Prove that:
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev   [CBSE 2019 (30/5/1)]
Ans: 
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev

Q 7. If cos θ + sin θ = √2cos θ , show that cos θ - sin θ = √2 sin θ.  

[CBSE 2019 (30/ 5/ 1)]
Ans: Given: cos θ + sin θ = √2cos θ

Now, (cos θ + sin θ)2 + ( cos θ - sin θ)2 
cos2θ + sin2θ + 2cosθ. sin θ + cos2θ + sin2θ - 2cosθ. sinθ
1 + 1 = 2

Again, (cos θ + sin θ)2 + (cos θ - sin θ)2 = 2
⇒ (√2 cosθ)2 + (cos θ - sin θ)2 = 2
⇒ 2 cos2θ + ( cos θ - sin θ)2 = 2
 ⇒ (cos θ - sin θ)2 = 2 - 2cos2θ = 2 ( 1 - cos2θ)
= 2sin2θ
∴ cos θ - sin θ = √2 sin θ
Hence proved

Q 8. Prove that: ( sin A + cosec A)2 + ( cos A + sec A)2 = 7 + tan2 A + cot2 4    

[CBSE 2019 (30/1/2;]

Ans: LHS = (sin A + cosec A)2 + (cos A + sec A)2 
=sin2 A + cosec2 A + 2sinA . cosec A + cos2 A + sec2 A + 2 cos A .sec A
= (sin2 A + cosec2 A + 2) + (cos2 A + sec2 A + 2)     (sin A.cosec A = 1)
= (sin2 A + cos2A) + (cosec2 A + sec2 A) + 4      (cos A. sec A = 1)
= 1 + 1+ cot2 A + 1 + tan2 A + 4
= 7 + tan2 A + cot2 A = RHS (∵ 1 + cot2 A = cosec2 A and 1 + tan2 A = sec2 A)

Q 9 . Evaluate:Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev   [CBSE 2019 (30/5/2)]
Ans:  We have,
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev

Q 10.  If sin (A + 2B)  Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev and cos (A + 4B) = 0, A > B, and A + 4B ≤ 900 then find A and B. [CBSE 2018 (C)]
Ans: Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev
So, sin(A + 2B) = sin 60°
Hence A + 2B = 60°     ..(i)
Also, we have
cos(A + 4B) = 0
cos(A + 4B) = cos 90°
A + 4B = 90°     ..(ii)
Subtracting (ii) from (i), we have
-2B = - 30°
=> B = 15°
Put B = 15° in eq. (i),  we have
A + 2(15°) = 60°
⇒ A + 30° = 60°
⇒ A = 30°

Q 11. If tan 2A = cot (A - 18°), where 2A is an acute angle, find the value of A.      [CBSE 2018]
Ans: tan 2A = cot (A - 18°)
⇒ cot (90° - 2A) = cot (A - 18°)
[∵ cot (90° — 0) — tan θ]
⇒ 90° - 2A = A - 18°
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev
∴ ∠A = 36°

Q 12. A, B, C are interior angles of ΔABC. Prove that Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev   

[CBSE, 2018 (C)]
Ans: As A + B + C = 180° ⇒ A + B = 180° - C
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev


Long Answer Type Questions

Q 1.  Prove that: Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev [CBSE 2019 (30/5/1)]
Ans: LHS

Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev

Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev

Q 2. Prove that:  Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev   [CBSE 2019 (30/5/1)]
Ans: LHS
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev
Previous Year Questions - Introduction to Trigonometry Class 10 Notes | EduRev


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