PREV YEAR QUESTIONS
1. If cosec 29/21 * where 0 < theta < 90 deg then what is the value of 4sec4tant?
1 11. If sine and tane = and tand then in which quadrant does @lie?
(a) 5
(b) 10
(c) 15
[NDA (II)-2019]
(d) 20
[NDA (I)-2019]
(a) First
(b) Second
2. Consider the following sttements:
(c) Third
1. cose + seco can never be equal to 1.5 2. tane + cote cannever be less than 2
(d) Fourth
[NDA (II)-2019)
(a) I only
(c) Both 1 and 2
(b) 2 only
(d) Neither 1 nor 2
12. If sine + cose 2 cose cose sind equalto then what
[NDA (I)-2019]
(b)- sine
(c) sin
(d) 2 sin
[NDA (II)-2019]
3. What is the length of the chord of a unit circle which subtends an angle at the centre?
(a) r * binomial(6,3)
(c) 2sin [[6], [2]]
(b)cos * binomial(9,2)
(d) s * [[theta], [2]]
4. if tanA = tan B = x , and cot A = y then what is the value of cot(A-B)?
(a) 1/x + 1/y
(b phi * 1/y - 1/x
(d) * 1 + 1/(xy)
[NDA (II)-2019]
5. What sin(a+)-2sinaros+sin(a-)
13. In a circle of diameter 44 cm, the length of chord is 22cm. What is the length of minor are of the chord?
NDA (1)-2019]
(a) 484/21 * cm
(C 121/21 * cm
14. What tanx tan)+tan) - secia sec equal to ?
(a) 0
(b) 1
[NDA (1)-2019)
(d) 4
15. If pecoseco-cote and q= (cosec + cot) then whichane of the followingis correct?
(c) 2
to? 6. If 2tanA=3tanB = 1, then what is tan(A-B)
(a) 1/5
(b) 1/6
(c) 1/7
[NDA (II)-2019]
(d) 1/9
[NDA (II)-2019)
(d)-19
[NDA (II)-2019]
(a) tanA
(b) cotA
(c) 2tanA
(d) 2cotA
[NDA (II)-2019]
(2)0
(c) 2sin
(b) 2sina
(d) sina + sin
equal
7. What is cos80+ cos40-cos20° equal to?
(a) 2 (b) 1 8. What is cot(A/2)-tan (A/2) equal to ?
(c)0
9. What is cotA+ cosec A equal to?
(c np + q = 1
16. of
[NDA (1)-2019]
(b) P = q
(d) * p + q = 0
sin34°cos 236-sin 56°sin124 cos 28°cos88+ cos 178° sin 208"
[NDA (I)-2019]
(d) 1
(a) pq = 1
(a) - 2 17. can as
(c)2
[NDA (I)-2019]
(a) (sin 9 deg + cos 9 deg)/(sin 9 deg - cos 9 deg)
(b) (sin Theta' - cos 9 deg)/(sin Theta' + cos 9 deg)
(c) (cos 9 deg + sin 9 deg)/(cos 9 deg - sin 9 deg)
(d)
[NDA (II)-2019]
(b) cox binomial(6,2)
(c) 2 ar(6/2)
(d) 2cot(6/7)
10. What tan25tan 15 tan + tan25 tan50° equal to?
Consider the following for next three) items:
Ifp = X cos Y sint, q = X sine + Y cose and p² + 4pq + q ^ 2 = A * X ^ 2 + B * Y ^ 2 * 0 <= 8 \le
18. What is the value
) pi/4
pi/3 ()
[NDA (1)-2019]
(d pi/6
(a) 0
(b) 1
(c) 2
[NDA (II)-2019]
(d) 4
Here are the step-by-step solutions to the Previous Year NDA (2019) Trigonometry questions you provided.
1. If \csc\theta = \frac{29}{21} (0 < \theta < 90^\circ), value of 4\sec\theta + 4\tan\theta
Given \sin\theta = \frac{21}{29} (since \sin = 1/\csc).
Using Pythagoras: \text{Base} = \sqrt{29^2 - 21^2} = \sqrt{841 - 441} = \sqrt{400} = 20.
\sec\theta = \frac{29}{20} and \tan\theta = \frac{21}{20}.
Expression: 4(\frac{29}{20}) + 4(\frac{21}{20}) = \frac{29}{5} + \frac{21}{5} = \frac{50}{5} = \mathbf{10}.
Correct Option: (b)
2. Consider the Statements
\cos\theta + \sec\theta can never be 1.5: For positive values, the sum of a number and its reciprocal (x + 1/x) is always \ge 2. Since 1.5 < 2, this statement is Correct.
\tan\theta + \cot\theta can never be less than 2: Similarly, by AM-GM inequality, x + 1/x \ge 2. So it cannot be less than 2. This statement is Correct.
Correct Option: (c) Both 1 and 2
3. Length of chord of a unit circle with angle \theta
Formula for chord length L = 2r \sin(\theta/2).
Since it is a unit circle, r = 1.
L = 2 \sin(\theta/2).
Correct Option: (c)
4. If \tan A = x, \tan B = y, value of \cot(A-B)
We know \tan(A-B) = \frac{\tan A - \tan B}{1 + \tan A \tan B} = \frac{x - y}{1 + xy}.
\cot(A-B) = \frac{1}{\tan(A-B)} = \frac{1 + xy}{x - y}.
Dividing numerator and denominator by xy: \frac{1/xy + 1}{1/y - 1/x}.
Correct Option: (c) (Matches the structure \frac{xy+1}{x-y})
6. If 2\tan A = 1 and 3\tan B = 1, find \tan(A-B)
\tan A = 1/2, \tan B = 1/3.
\tan(A-B) = \frac{1/2 - 1/3}{1 + (1/2 \cdot 1/3)} = \frac{1/6}{1 + 1/6} = \frac{1/6}{7/6} = \mathbf{1/7}.
Correct Option: (c)
7. Value of \cos 80^\circ + \cos 40^\circ - \cos 20^\circ
Use \cos C + \cos D: \cos 80^\circ + \cos 40^\circ = 2\cos 60^\circ \cos 20^\circ.
Since \cos 60^\circ = 1/2, it becomes 2(1/2) \cos 20^\circ = \cos 20^\circ.
\cos 20^\circ - \cos 20^\circ = \mathbf{0}.
Correct Option: (c)
8. \cot(A/2) - \tan(A/2)
\frac{\cos(A/2)}{\sin(A/2)} - \frac{\sin(A/2)}{\cos(A/2)} = \frac{\cos^2(A/2) - \sin^2(A/2)}{\sin(A/2)\cos(A/2)}.
Numerator is \cos A. Denominator is \frac{1}{2}\sin A.
Result: 2 \frac{\cos A}{\sin A} = \mathbf{2\cot A}.
Correct Option: (d)
11. In which quadrant does \theta lie if \sin\theta = -1/2 and \tan\theta = 1/\sqrt{3}?
\sin\theta is negative in 3rd and 4th quadrants.
\tan\theta is positive in 1st and 3rd quadrants.
Common quadrant is the Third.
Correct Option: (c)
13. Length of minor arc
Diameter = 44 cm \rightarrow Radius (r) = 22 cm.
Chord = 22 cm.
Since r = r = \text{chord}, it forms an equilateral triangle. Central angle \theta = 60^\circ = \pi/3 radians.
Arc length l = r\theta = 22 \times (\pi/3) = 22 \times \frac{22}{7 \times 3} = \frac{484}{21} cm.
Correct Option: (a)
15. Relation between p = \csc\theta - \cot\theta and q = (\csc\theta + \cot\theta)^{-1}
We know \csc^2\theta - \cot^2\theta = 1, which means (\csc\theta - \cot\theta)(\csc\theta + \cot\theta) = 1.
So, (\csc\theta - \cot\theta) = \frac{1}{\csc\theta + \cot\theta}.
This means p = q.
Correct Option: (b)
Would you like me to solve the remaining specific questions from the list (like 16, 17, or 18) in more detail?