Sscglpinnacle Dhaka

SSC CGL TIER-1 Previous Year Trigonometry TCS Questions & Solutions

Validity: 9 Months
What you will get
Course Highlights
  • Based on latest Pattern
  • English Medium eBooks
Already Bookmark
SSC

SSC CGL TIER-1 Previous Year Trigonometry TCS Questions & Solutions 

SSC CGL T-2 2019 SSC CGL T-1 2019 SSC CHSL 2019 SSC CPO 2020 SSC MTS 2019
SSC CGL T-2 2018 SSC CGL T-1 2018 SSC CHSL 2018 SSC CPO 2019 SSC MTS 2017

Q1. If x = 4cosA + 5sinA and y = 4 sinA - 5 cosA,then the value of

x2 +y2 is

यदि x = 4cosA + 5sinA तथा y = 4 sinA - 5 cosA है, 

तो x2 +y2 का मान क्या होगा ? 

SSC CGL 3 March 2020 (Morning)

(a) 41

(b) 0

(c) 16

(d) 25

Q2. If A lies in the first quadrant and 6tanA = 5, then the value

is

यदि A प्रथम चतुर्थांश में स्थित है तथा 6tanA = 5 है, तो  का मान क्या होगा ? 

SSC CGL 3 March 2020 (Morning)

(a) -2

(b) 1

(c) 16

(d) 4

Q3. If A+B = 45°, then the value of 2(1+ tanA)(1+ tanB) is:

यदि A+B = 45° है, तो 2(1+ tanA)(1+ tanB) का मान होगा : 

SSC CGL 3 March 2020 (Morning)

(a) 2

(b) 4

(c) 1

(d) 0

SSC 5000 MCQ Math TCS- chapter wise ebook bilingual questions till date with explanation and tricks SSC CGL Math online course 
SSC CGL Achievers Program  SSC CGL 100 Online tests- test Series 

Q4. If  2sinθ+15 cos2 θ=7, 0°<θ<90°, than tanθ+cosθ+ secθ =

यदि  2sinθ+15 cos2 θ=7, 0°<θ<90° है, तो tanθ+cosθ+ secθ = ?

SSC CGL 3 March 2020 (Afternoon)

  (d) 4

Q6. The value of the expression cosec(85°+θ) - sec(5°-θ) - tan(55°+θ) + cot(35°- θ) is:

व्यंजक cosec(85° + θ) - sec(5°-θ) - tan(55°+θ) + cot(35°- θ) का मान है : 

SSC CGL 3 March 2020 (Afternoon)

(a)3/2 

(b) 0

(c) -1

(d)1

Q8. If 2 sinθ - 8 cos2θ + 5 = 0, 0°<θ<90°, then what is the value of (tan 2θ + cosec 2θ)?

यदि 2 sinθ - 8 cos2θ + 5 = 0, 0°<θ<90° है, तो (tan 2θ + cosec 2θ) का मान क्या होगा ? 

SSC CGL 3 March 2020 (Evening)

Q9. In the figure, what is the value of cotθ?

इस आकृति में, cotθ का मान कितना है? 

Q10. If secθ - tanθ =,(0<x<y) and 0°<θ<90°, then sinθ is equal to:

यदि secθ - tanθ =   (0<x<y) तथा 0°<θ<90° है, तो sinθ का मान किसके बराबर है ? 

SSC CGL 4 March 2020 (Morning)

SSC CGL 4 March 2020 (Afternoon)

(a) -2

(b) 1

(c) 2

(d) -1

Q16. If secθ + tanθ = p, 0°<θ<90°, then

is equal to:

यदि secθ + tanθ = p है, जहाँ  0°<θ<90° है, तो

  का मान किसके बराबर होगा ? 

SSC CGL 4 March 2020 (Evening)

(a) cosecθ

(b) sinθ

(c) cosθ

(d) 2cosecθ

 

SSC CGL 5 March 2020 (Afternoon)

(a) 0

(b) 2

(c) -1

(d) 1

Q26. The value of cos 0°cos 30°cos 45°cos 60°cos 90° is:

cos 0°cos 30°cos 45°cos 60°cos 90° का मान क्या होगा? 

SSC CGL 5 March 2020 (Evening)

(a) 5

(b) 

(c) 3

(d) 0

Q28. If xcosA - ysinA = 1 and xsinA + ycosA = 4, then the value of 17x2 +17y2 is:

यदि xcosA - ysinA = 1 तथा xsinA + ycosA = 4 है, तो  17x2 +17y2 का मान क्या होगा ? 

SSC CGL 6 March 2020 (Morning)

(a) 0

(b) 49

(c) 7

(d) 289

Q29. If (2sin A + cosec A) = 2√2, 0°<A<90°, then the value of 2(sin4A+cos4 A) is:

यदि (2sin A + cosec A) = 2√2, 0°<A<90° है, तो  2(sin4A+cos4 A) का मान क्या होगा ? 

SSC CGL 6 March 2020 (Morning)

(a) 1

(b) 2

(c) 4

(d) 0

SSC CGL 6 March 2020 (Morning)

(a) -1

(b) -2

(c) 1

(d) 2

Q31. Solve the following/ हल कीजिए : 

 sin 0° sin 30° sin 45° sin 60° sin 90° = ?

SSC CGL 6 March 2020 (Afternoon)

(a) 0

(b) 

(c) 1

(d) 4

Q32. If (cos2θ-1)(1+tan2 θ) +2tan2 θ  = 1, 0°<θ<90°, then θ is 

यदि  (cos2θ-1)(1+tan2 θ) +2tan2 θ  = 1 है, जहाँ 0°<θ<90°, तो  θ का मान होगा : 

SSC CGL 6 March 2020 (Afternoon)

(a) 45°

(b) 60°

(c) 30°

(d) 90°

 

SSC CGL 6 March 2020 (Evening)

(a) 2

(b) 4

(c) 8

(d) 1

Q37. The value of is:

का मान है : 

SSC CGL 7 March 2020 (Morning)

(a) -2sin2θcos2θ

(b) -1

(c) 0

(d) 1

Q38. What is the value of sin 30°+cos 30°-tan 45°?

sin 30°+cos 30°-tan 45° का मान क्या होगा?

SSC CGL 7 March 2020 (Morning)

Q39. In the given figure, cosθ is equal to: 

दी गयी आकृति में, cosθ  किसके बराबर है ? 

Q40. If 3sec2 θ+tanθ=7, 0°<θ<90°, then the value of 

Q42. If cotθ + tanθ = 2secθ, 0°<θ<90°, then the value of

Q43. If 5cos2 θ+1=3sin2θ, 0°<θ<90°, then what is the value of 

Q44. Solve the following/ निम्नलिखित को हल कीजिए  

SSC CGL 7 March 2020 (Evening)

(a) 2

(b) 1

(c) 0

(d) -1

Q45. In the right triangle shown in the figure, what is the value of cosecθ?

 इस आकृति में दिए गए समकोण त्रिभुज में, cosecθ का मान क्या है ? 

Q46. If 6tanθ-5√3secθ+12 cotθ = 0, 0°<θ<90°, then the value of (cosecθ+secθ) is: 

यदि 6tanθ-5√3secθ+12 cotθ = 0, 0°<θ<90° है, तो (cosecθ+secθ) का मान क्या होगा ? 

SSC CGL 9 March 2020 (Morning)

Q47. The value of (cosecA + cotA +1)(cosecA - cotA + 1) - 2cosecA is: 

(cosecA + cotA +1)(cosecA - cotA + 1) - 2cosecA का मान है : 

SSC CGL 9 March 2020 (Afternoon)

(a) 4cosecA

(b) 2

(c) 2cosecA

(d) 0

Q48. If 5 cotθ = 3, find the value of 

Q49. Solve the following/ हल कीजिए | 

SSC CGL 9 March 2020 (Afternoon)

(a) 1
(b) 3

(c) 0
(d) 2

Q50. The value of is: 

का मान क्या होगा ? 

SSC CGL 9 March 2020 (Evening)

(a) 4

(b) 3

(c) 1

(d) 2

Q51. The value of cos 10° cos 30° cos 50° cos 70° cos 90° is:

cos 10° cos 30° cos 50° cos 70° cos 90° का मान है :

SSC CGL 9 March 2020 (Evening)

(a) 3

(b) 0

(c) 5

(d) 1

Q52. The value of (cosec 30° - tan 45°)cot 60° tan 30° is:

(cosec 30° - tan 45°)cot 60° tan 30° का मान क्या है?  

SSC CGL 9 March 2020 (Evening)

(a) 13

(b) 1

(c) 3

Here are the solutions to the above questions of trigonometry asked in the SSC exam asked by TCS. Some questions have alternate solutions.

Sol 1. (a)  x= 4cosA + 5sinA

y= 4sinA - 5cosA

x2 = 16cos2 A + 25sin2 A + 40 cosA sinA

y2 = 16sin2 A + 25cos2 A - 40 cosA sinA

x2 +y2 = 16(cos2 A + sin2 A) + 25(sin2 A + cos2 A)= 41

Sol 2. (b) 

Sol 3. (b) We know that, if x+y = 45° than (1+ tanx)(1+ tany) = 2

Here A+B= 45°

Then,

2(1+ tanA)(1+ tanB)= 4

Sol 4. (a)  2sinθ+15 cos2θ=7, 0°<θ<90°

  2sinθ+15(1-sin2θ)=7

15 sin2θ-2sinθ-8=0

Sol 5. (b) It is given that

Sol 6. (b) Put θ= 5° in given equation: cosec(85°+θ)-sec(5°-θ)-tan(55°+θ)+cot(35°-θ)

We get:

Cosec 90°- sec0° - tan60° + cot30°

1-1-√3+√ 3

0

Sol 7. (a)

Sol 8. (d) It is given that 

2 sinθ - 8 cos2θ + 5 = 0

And 0°<θ<90°

cos2θ= 1- sin2θ

2 sinθ - 8 cos2θ + 5 = 0

2 sinθ - 8(1-sin2θ)+5 = 0

8sin2θ + 2 sinθ - 3 =0

Solve the quadratic equation, we get

Sinθ = 1/2 or -3/4

Sinθ can not be negative for 0°<θ<90°

Thus θ= 30°

Now, tan 2θ + cosec 2θ = tan 60°+ cosec 60°

Sol 14. (d) 3sec2θ tan2θ + tan6 θ- sec6θ = ?

We know that: sec2θ-tan2θ = 1

Cubing both sides we get:

Sec6θ - tan6θ - 3sec2θtan2θ = 1

Thus,

 3sec2θ tan2θ + tan6θ- sec6θ = -1

Only option (c) satisfies.

Sol 16. (b) secθ+tanθ = p

Sol 17. (a) 7cos2θ+3sin2θ=6, 0°<θ<90°

sin2θ = 1-cos2θ

4cos2θ = 3

Sol 19.

 (d) 12cos2θ-2sin2θ+3cosθ = 3, 0°<θ<90°

Put sinθ = 1 - cos2θ

We get:

14 cos2θ + 3 cosθ -5 = 0

Sol 22. (b) 11sin2θ-cos2θ+4sinθ-4=0 , 0°<θ<90°

Cos2θ = 1 - sin2θ

11 sin2θ -1 + sin2θ + 4 sinθ - 4 = 0

12 sin2θ + 4 sinθ - 5 = 0

Sinθ = 1/2θ = 30°

Sol 26. (d) cos 0°cos 30°cos 45°cos 60°cos 90° = 0

Sol 27. (d) tanθ-cotθ = cosecθ, 0°<θ<90°

At θ = 60°, tanθ-cotθ = cosecθ

[cos 90° = 0]

Sol 28. (d) xcosA - ysinA = 1 and xsinA + ycosA = 4

(x2+y2)(sin2A+cos2A) = (1+16) = 17

17(x2+y2) = 289

Sol 29. (a) 2sin A + cosec A = 2√2, at A = 45°

Then, 2(sin4 A+cos4A) = 1

Sol 31. (a) sin 0° sin 30° sin 45° sin 60° sin 90° = 0 (sin 0° = 0)

Sol 32. (a) (cos2θ-1)(1+tan2θ) +2 tan2θ = 1, 0°<θ<90°

(-sin2θ)(sec2θ) +2 tan2θ = 1

-tan2θ+2tan2θ = 1

tan2θ = 1

θ = 45°

Sol 33. (a)

Sol 35. (b) In the third quadrant tanA and cotA are positive.

Sol 38. (a) sin 30°+ cos 30°- tan 45°

Sol 47. (b) ([cosecA+cotA]+1)([cosecA-cotA]+1)-2cosecA

cosec2A-cot2A+cosecA+cotA+cosecA-cotA+1-2cosecA

1+2cosecA+1-2cosecA

2

Sol 51. (b) cos 90° = 0 

Therefore, 

cos10°cos30°cos50°cos70°cos90° = 0

Sol 52 (a) (cosec 30°-tan 45°)cot 60°tan 30° 

 SSC previous year questions 

Thanks for reading. If it is useful for you please share it with your friends. 

You should follow us on 

Youtube Channel Telegram Channel Whatsapp Facebook Page
Facebook Group Frontier IAS website Frontier IAS Youtube Channel Frontier IAS Facebook page

You may like similar articles on this website 

  1. All GK questions asked by TCS in SSC exams subject wise 
  2. All Reasoning Questions asked by TCS in SSC exams chapter wise
  3. All English Questions asked by TCS in SSC exams Chapter wise 
  4. Ebooks of all TCS questions previous years of all subjects 
  5. SSC CGL Tier 1 Practice papers
  6. SSC CGL Tier 2 Practice papers