Trigonometry Questions for Competitive Exams

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Trigonometry Questions for Competitive Exams

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Trigonometry Questions for Competitive Exams for SSC, BANK, AND RAILWAYS are very Simple and Easy. We also Cover Basic Topics like math,  etc, and study materials including Previous Year Question Papers, Current Affairs, Important Formulas, etc for upcoming Banking, UPSC, and SSC CGL Exams. Our PDF will help you to upgrade your marks in any competitive exam.

 

     Topic Related posts 

     Trigonometry

  • The Pythagorean Theorem.
  • Special Right Triangles.
  • Basic Trigonometric Functions.
  • Solving Right Triangles.
  • Measuring Rotation.
  • Applying Trig Functions to Angles of Rotation.
  • Trigonometric Functions of Any Angle.
  • Relating Trigonometric Functions.

Trigonometry Questions for Competitive Exams

Trigonometry Questions for SSC Exams

Q.1: यदि (sin A – cos A) = 0 है, तो cot A का मान ज्ञात करें
(A) \frac{\pi}{6}
(B) 0
(C) 1
(D) \frac{\pi}{4}
(SSC CHSL Aug 2021)

Ans : (C) 1
(sin A – cos A) = 0
sin A = cos A
\frac{cos A}{sin A} = 1
cot A = 1

Q.2: यदि cosec\theta=\frac{41}{9} है और \theta न्यून कोण है, तो 5 tan\theta का मान ज्ञात करें
(A) \frac 98
(B) \frac {11}{8}
(C) \frac {13}{4}
(D) \frac 78
(SSC CHSL Aug 2021)

Ans : (A) \frac 98
cosec\theta=\frac{41}{9}
sin\theta=\frac{9}{41}
पाइथागोरस प्रमेय से
BC2 = 41– 92
BC =\sqrt{1600} = 40
ATQ 5 tan\theta = 5\times \frac{9}{40}
=\frac98

Q.3: निम्न समीकरण में\theta का मान ज्ञात करें
3 cot\theta + tan \theta -2\sqrt3 = 0,0 <\theta < 90^o
(A) 60o
(B) 30o
(C) 15o
(D) 45o
(SSC CHSL Aug 2021)Ans : (A) 60o
3 cot\theta + tan \theta -2\sqrt3 = 0
Put \theta = 60 its satisfy
3 x cot60 + tan60 -2 \sqrt{3}
3\times\frac{1}{\sqrt3} +\sqrt3 - 2\sqrt3
\frac{3}{\sqrt3} +\sqrt3 - 2\sqrt3
\frac{6}{\sqrt3} -2\sqrt3
\frac {6-6}{\sqrt3} = \frac{0}{\sqrt3} = 0
so \theta = 60

 

Q.4: \triangle ABC में, \angle A = 90^0, AB = 20cm और BC = 29cm है l (sinB -cotC) का मान ज्ञात करें l
(A) \frac{189}{580}
(B) -\frac {9}{29}
(C) \frac{9}{29}
(D) -\frac{189}{580}
(SSC CHSL Aug 2021)

Ans : (D) -\frac{189}{580} 

trigonometry questions for ssc

Q.5: यदि tanx = cot(48o + 2x) और 0o <x <90o है, तो x का मान ज्ञात करें
(A) 14o
(B 12o
(C) 21o
(D) 16o
(SSC CHSL Aug 2021)

Ans : (A) 14o
tan x = cot (48 + 2x)
tanx = tan (90 – (48 + 2x)
x = 90 -(48 + 2x)
x = 90 – 48 – 2x
3x = 42
x = 14

Q.6: यदि 7 sin^2\theta + 3cos^2\theta = 4,0^o <\theta <90^o है, तो \theta का मान ज्ञात करें l
(A) 45o
(B) 30o
(C) 60o
(D) 75o
(SSC CHSL Aug 2021)

Ans : (B) 30o
7 sin^2\theta + 3cos^2\theta = 4
4 sin^2\theta + 3sin^2\theta +3cos^2\theta= 4
4 sin^2\theta + 3(sin^2 \theta + cos^2\theta)= 4
4sin^2\theta + 3\times1 = 4
4sin^2\theta = 4 - 3 = 1
sin^2\theta =\frac 14
sin\theta =\frac 12
\theta = 30^o

Q.7: \theta का मान ज्ञात करें, यदि sec^2\theta +(1 -\sqrt3)tan\theta -(1 +\sqrt3)=0, जहां \theta न्यून कोण है l
(A) 30o
(B) 15o
(C) 60o
(D) 45o
(SSC CHSL Aug 2021)

Ans : (C) 60o
sec^2\theta +(1 -\sqrt3) tan\theta -(1 +\sqrt3) =0
put \theta = 60^o (By option)
sec^2(60) + (1 -\sqrt3) tan 60 - (1 +\sqrt3)
4 +(1 - \sqrt3) \sqrt3 - (1 + \sqrt3)
4 +\sqrt3 - 3 - 1 -\sqrt3
4 – 4 = 0
So \theta = 60

Q.8: यदि cos\theta =\frac{7}{3\sqrt6} है और \theta न्यून कोण है, तो 27 sin^2\theta -\frac 32 का मान ज्ञात करें l
(A) 15
(B) 12
(C) 1
(D) 9
(SSC CHSL Aug 2021)

Ans : (C) 1 

trigonometry questions for ssc

Q.9: C पर समकोण त्रिभुज ABC में यदि sec A=\frac{13}{5} हो, तो \frac{1+ sinA}{cosB} का मान ज्ञात करें l
(A) \frac{18}{5}
(B) 5
(C) \frac32
(D) \frac{25}{12}
(SSC CHSL Aug 2021)

Ans : (D) \frac{25}{12} 

Q.10: यदि sin\theta + cosec \theta = 7है, तो sin^3\theta + cosec^3\theta का मान ज्ञात कीजिए l
(A) 322
(B) 382
(C) 367
(D) 350
(SSC CHSL Aug 2021)

Ans : (A) 322
sin\theta + cosec \theta = 7
(sin\theta + cosec \theta)^3 = 7^3
sin^3\theta + cosec^3 \theta +3sin\theta cosec\theta\times7 = 343
sin^3\theta + cosec^3 \theta +3\times7 = 343 [Sin\theta\times Cosec\theta = 1]
sin^3\theta + cosec^3\theta = 343 - 21 = 322

Q.11: यदि 3 cot A = 4 tan A है, तथा A एक न्यून कोण है, तो Sec A का मान ज्ञात करें l
(A) \frac{\sqrt7}{2}
(B) \frac{1}{\sqrt3}
(C) \frac12
(D) \frac{\sqrt21}{3}
(SSC CHSL Aug 2021)

 

Ans : (A) \frac{\sqrt7}{2} 

trigonometry questions for ssc

Q.12: \frac{cos^220^o + cos^270^o}{sin^290^o} -tan^245^o का मान ज्ञात करें l
(A) -1
(B) 0
(C) -2
(D) 1
(SSC CHSL Aug 2021)

Ans : (B) 0
\frac{cos^220^o + cos^270^o}{sin^290^o} -tan^245^o
\frac{1}{1} -1 [Cos220 + Cos270 = 1, tan 45 = 1]= 0

Q.13: यदि \sqrt{13} Sin \theta = 2 हैं, तो \frac{3tan\theta +\sqrt{13}Sin\theta}{\sqrt{13}Cos \theta-3 tan \theta} का मान क्या होगा ?
(A) 5
(B) \frac 12
(C) 3
(D) 4
(SSC CHSL Aug 2021)

Ans : (D) 4 

Q.14: C पर समकोण वाले एक समकोण त्रिभुज ABC में, Sin A = Sin B है l Cos A का मान ज्ञात करें l
(A) 1
(B) \frac{\sqrt3}{2}
(C) \frac 12
(D) \frac{1}{\sqrt2}
(SSC CHSL Aug 2021)

Ans : (D) \frac{1}{\sqrt2}
Sin A = Sin B
A = B = 45 Satisfy
Cos A = Cos 45
\frac{1}{\sqrt2}

Q.15: यदि 5 Cos \theta = 4 Sin \theta , 0^o \leq \theta \leq 90^o है, तो Sec \theta का मान ज्ञात करें l
(A) \frac{\sqrt{41}}{4}
(B) \frac{\sqrt{41}}{16}
(C) \frac{\sqrt{41}}{5}
(D) \frac35
(SSC CHSL Aug 2021)

Ans : (A) \frac{\sqrt{41}}{4} 

Q.16: \frac{Cos 8^o Cos 24^o Cos 60^o Cos 66^o Cos 82^o}{Sin 82^o Sin 66^o Sin 60^o Sin 8^o Sin 24^o} का मान कितना होगा ?
(A) \frac{1}{\sqrt2}
(B) \frac{1}{\sqrt3}
(C) 1
(D) 0
(SSC CHSL Aug 2021)

Ans : (B) \frac{1}{\sqrt3}
Cos 8o Cos 82o = 1
Cos 24o Cos 66o = 1
Sin 82o Sin 8o = 1
Sin 66o Sin 24o = 1
so \frac{Cos 60^o}{Sin 60^o}
Cot 60=\frac{1}{\sqrt3}

Q.17: यदि Sin B =\frac{9}{41} है, तो Cot B का मान क्या होगा, जहां 0o <B <90o है ?
(A) \frac{9}{41}
(B) \frac{41}{9}
(C) \frac{9}{40}
(D) \frac{40}{9}
(SSC CHSL Aug 2021)

Ans : (D) \frac{40}{9} 

Q.18: यदि tan\theta =\frac43 है, तो \frac{9 Sin\theta + 12 Cos \theta}{27 Cos\theta -20sin \theta} का मान ज्ञात करें l
(A) 36
(B) 100
(C) 18
(D) 72
(SSC CHSL Aug 2021)

Ans : (D) 72 

trigonometry questions for ssc

Q If cos θ = , then tan θ is equal to.

(A)

(B)

(C)

(D) 3

Correct Answer : D

Q :   If 2sin2 θ – 3 sin θ + 1 = 0,   θ being positive angle, then the values of θ are :

(A)

(B)

(C)

(D)

Correct Answer : A

 

Q :  If tan α = 2, then the value of   αααα is :

(A)

(B)

(C)

(D)

Correct Answer : C

 

Q :   What is the value of  is:

(A) 3

(B) 2

(C) 1

(D) 0

Correct Answer : C

Q :   A tower standing on a horizontal plane subtends a certain angle at a point 160 m apart from the foot of the tower. On advancing 100 m towards it, the tower is found to subtend and angle twice as before. The height of the tower is

(A) 80 m

(B) 100 m

(C) 160 m

(D) 200 m

Correct Answer : A

Q :   If sinθ – cosθ = 7/13 and 00 < θ < 900 , then the value of sinθ + cosθ is :

(A) 17/13

(B) 13/17

(C) 1/13

(D) 1/17

Correct Answer : A

 

What is the value of

(A) 0

(B) 1

(C) -1

(D) 2

Correct Answer : B

 

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