Trigonometry Questions for Competitive Exams

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.

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 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) $-\frac{189}{580}$

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

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 $sin\theta + cosec \theta = 7$है, 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) $\frac{\sqrt7}{2}$

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

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

(A)

(B)

(C)

(D) 3

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

(A)

(B)

(C)

(D)

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

(A)

(B)

(C)

(D)

Q :   What is the value of  is:

(A) 3

(B) 2

(C) 1

(D) 0

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

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

What is the value of

(A) 0

(B) 1

(C) -1

(D) 2

General Science Notes

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