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Trigonometry Questions and Answers

Q1 :

The value of θ(0≤θ≤π2)theta left(0 leq theta leq frac{pi}{2} right) satisfying the equation

sin2θ−2 cosθ+14=0 , istext{sin}^2 theta - 2 text{ cos} theta + frac{1}{4} = 0 text{ , is}

A
  

π2frac{pi}{2}

B
  

π3frac{pi}{3}

C
  

π4frac{pi}{4}

D
  

π6frac{pi}{6}

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Q2 :

The expression for sin θtheta in terms of sec

A
  

1 sec2θ−1frac{1}{sqrt{text{ sec}^2 theta - 1 }}

B
  

 sec2θ sec2θ−1frac{text{ sec}^2 theta}{sqrt{text{ sec}^2 theta - 1 }}

C
  

 sec2θ−1 secθfrac{sqrt{text{ sec}^2 theta - 1 }}{text{ sec} theta}

D
  

 sec2θ−1sqrt{text{ sec}^2 theta - 1 }

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Q3 :

The value of sin 45∘+ sin 105∘+ cos 105∘ cos 45∘sin 75∘+ cos 75∘frac{text{sin } 45^circ + text{ sin } 105^circ + text{ cos } 105^circ text{ cos } 45^circ} { text{sin } 75^circ + text{ cos } 75^circ }is equal to

A
  

16frac{1}{sqrt6}

B
  

13frac{1}{sqrt3}

C
  

123frac{1}{2sqrt3}

D
  

132frac{1}{3sqrt2}

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Q4 :

If  tanx+cotx=3,then sec2x+cosec2xtext{ tan}x + text{cot}x = 3, text{then sec}^2x + text{cosec}^2x is equal to 

A
  

3

B
  

9

C
  

12

D
  

15

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Q5 :

Two boys are on opposite sides of a tower of 100 meter height. If they measure the elevation of the top of the tower as 30∘30^circ and 45∘45^circ respectively, the distance between the tower is 200 metres, then the distance between the boys is

A
  

1003 metres100sqrt3 text{ metres}

B
  

100(3+1) metres100(sqrt3 +1) text{ metres}

C
  

100(3−1) metres100(sqrt3 -1) text{ metres}

D
  

1003−1 metres100sqrt3 -1 text{ metres}

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Q6 :

For λ≠0lambda ne 0, the angle between the lines given by the equation λy2+(1−λ2)xy−λx2=0lambda y^2 + (1 - lambda^2) ; xy - lambda x^2 = 0 is

A
  

30°30degree

B
  

45°45degree

C
  

60°60degree

D
  

90°90degree

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Q7 :

If cos α+sec α=2text{cos } alpha + text{sec } alpha = 2, then the value of cos8α+sec8αtext{cos}^8 alpha + text{sec}^8 alpha is equal to

A
  

22

B
  

222^2

C
  

242^4

D
  

282^8

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Q8 :

The numerical value of the expression

sin9°sin48°−cos81°cos42°dfrac{text{sin}9degree}{text{sin}48degree} - dfrac{text{cos}81degree}{text{cos}42degree}sin9°sin48°−cos81°cos42°frac{text{sin}9degree}{text{sin}48degree} - frac{text{cos}81degree}{text{cos}42degree}  is

A
  

1

B
  

1/2

C
  

0

D
  

-1

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Q9 :

An angle is divided into two parts αalpha and βbeta in such αalpha way that  tan⁡α=12tan alpha = frac{1}{2} and tan⁡β=2tan beta = 2. The measure of the angle is

A
  

2π3frac{2pi}{3}

B
  

π2frac{pi}{2}

C
  

πpi

D
  

3π4frac{3pi}{4}

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Q10 :

If α+β=90°alpha + beta = 90degree, then cosec2α+cosec2βtext{cosec}^2alpha + text{cosec}^2beta is equal to

A
  

cosec2α+cosec2βtext{cosec}^2alpha + text{cosec}^2beta

B
  

sin2α+sin2βtext{sin}^2alpha + text{sin}^2beta

C
  

tan2α+tan2βtext{tan}^2alpha + text{tan}^2beta

D
  

sec2α+sec2βtext{sec}^2alpha + text{sec}^2beta

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Q11 :

If sin⁡2θ=cos⁡3θsin 2theta =cos 3theta and θtheta is an acute angle, then θtheta is equal to

A
  

18°18degree

B
  

27°27degree

C
  

36°36degree

D
  

45°45degree

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Q12 :

If sec 11θ= cosec 7θ(0°<θ<20°)11theta = text{ cosec } 7theta (0degree lt theta lt 20degree), then the value of θtheta is

A
  

5°5degree

B
  

10°10degree

C
  

15°15degree

D
  

18°18degree

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Q13 :

The maximum value of sin⁡θ⋅cos⁡θsin theta cdot cos theta is

A
  

1

B
  

12frac{1}{2}

C
  

12frac{1}{sqrt{2}}

D
  

32frac{sqrt{3}}{2}

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Q14 :

The value of sin⁡3(15°)−cos⁡3(15°)sin^3 (15degree) - cos^3 (15degree) is

A
  

34(sin⁡15°−cos⁡15°)frac{3}{4}(sin 15degree - cos 15degree )

B
  

582frac{5}{8sqrt{2}}

C
  

−582-frac{5}{8sqrt{2}}

D
  

−542-frac{5}{4sqrt{2}}

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Q15 :

The value of 3tan⁡20°−tan⁡320°1−3tan⁡220frac{3 tan 20degree - tan^3 20 degree}{1 - 3tan^2 20} is equal to

A
  

13frac{1}{sqrt{3}}

B
  

1

C
  

3sqrt{3}

D
  

23frac{2}{sqrt{3}}

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Q16 :

If 2cos⁡2θ+11sin⁡θ−7=02 cos^2 theta + 11 sin theta - 7 = 0, then  the value of sin⁡θsin theta is equal to

A
  

−12frac{-1}{2}

B
  

12frac{1}{2}

C
  

5

D
  

12frac{1}{sqrt{2}}

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Q17 :

The angle between the hour and minute hands of a clock at 02 : 15 hour is

A
  

15°15degree

B
  

712°7frac{1}{2}degree

C
  

2212°22frac{1}{2}degree

D
  

30°30degree

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Q18 :

An aeroplane at a height of 3000 m, passes vertically above another aeroplane at an instant. If the angles of elevation of the two aeroplanes from some point on the ground are 60°60degree and 45°45degree, respectively, then the vertical distance between the two planes is:

A
  

1000(3−1) m 1000 Big(sqrt{3 - 1}Big) text{ m }

B
  

10003 m 1000 sqrt{3} text{ m }

C
  

1000(3−3) m 1000 Big(3 - sqrt{3}Big) text{ m }

D
  

10003 m 1000 sqrt{3} text{ m }

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Q19 :

If tan⁡θ+sec⁡θ=2,0≤θ≤π2tan theta + sec theta = 2, 0 le theta le frac{pi}{2}; then the value of tan⁡θtantheta is equal to :

A
  

34frac{3}{4}

B
  

54frac{5}{4}

C
  

32frac{3}{2}

D
  

52frac{5}{2}

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Q20 :

The value of (cos⁡225°+cos⁡265°)(cos^2 25degree + cos^2 65degree) is:

A
  

0

B
  

sin⁡240°sin^2 40degree

C
  

cos⁡240°cos^2 40degree

D
  

1

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Q21 :

If cos⁡2θ−3cos⁡θ+2sin⁡2θ=1,θ,0frac{cos^2theta - 3costheta + 2}{sin^2theta} = 1, theta, 0 then θtheta is :

A
  

30°30degree

B
  

60°60degree

C
  

75°75degree

D
  

90°90degree

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Q22 :

If a and b are positive, then the relation sin⁡θ=(a+2b)/2b sin theta = (text{a} + 2text{b})/2text{b } is

A
  

not possible

B
  

possible only if a = b

C
  

possible if a < b

D
  

possible if b > a

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Q23 :

If the angle of elevation of the top of a tower at a distance 100 metres from its foot is 45°45degree, then the height, in metres, of the tower is equal to

A
  

100

B
  

75

C
  

4500

D
  

50

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Q24 :

The expression cos⁡3θ−sin⁡3θcos⁡θ−sin⁡θfrac{cos^3 theta - sin^3 theta}{cos theta - sin theta} simplifies to

A
  

1+sin⁡θ21 + frac{sin theta}{2}

B
  

1+sin⁡2θ21 + frac{sin 2 theta}{2}

C
  

1+sin⁡θ2frac{1 + sin theta}{2}

D
  

1+sin⁡2θ2frac{1 + sin 2 theta}{2}

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Q25 :

If tan A + cot A = 2, then the value of sec A, is equal to

A
  

11

B
  

2sqrt2

C
  

12frac{1}{2}

D
  

32frac{sqrt3}{2}

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