Trigonometric ratio Questions and answers

  1. Elementary Mathematics
    1. Area and perimeter
    2. Circles
    3. Clocks
    4. Factorisation
    5. Geometry
    6. Height and Distance
    7. Indices and Surd
    8. LCM and HCF
    9. Loci and concurrency
    10. Logarithms
    11. Polynomials
    12. Quadratic Equations
    13. Quadrilateral and parallelogram
    14. Rational expression
    15. Real Analysis
    16. Rectangular and Cartesian products
    17. Set theory
    18. Simple and Decimal fraction
    19. Simplification
    20. Statistics
    21. Straight lines
    22. Triangle
    23. Trigonometric ratio
    24. Trigonometry
    25. Volume and surface area
1). If \( \Large \sin \theta +cosec \theta =2,\ then\ \sin^{2} \theta + cosec^{2} \theta \)  is equal to
A). 1
B). 4
C). 2
D). none of these
2). The value of \( \Large \frac{\cot^{2} \theta +1}{\cot^{2} \theta -1} \) is equal to:
A). \( \Large \sin 2 \theta \)
B). \( \Large \cos 2 \theta \)
C). \( \Large \cosh 2 \theta \)
D). \( \Large \sec 2 \theta \)
3). If \( \Large \tan A = 2 \tan B + \cot B,\ then\ 2 \tan \left(A-B\right) \) is equal to:
A). \( \Large \tan B \)
B). \( \Large 2 \tan B \)
C). \( \Large \cot B \)
D). \( \Large 2 \cot B \)
4). If \( \Large \tan A - \tan B = x\ and\ \cot B - \cot A = y,\) then\( \Large  \cot \left(A-B\right) \) is equal to:
A). \( \Large \frac{1}{x}+y \)
B). \( \Large \frac{1}{xy} \)
C). \( \Large \frac{1}{x}-\frac{1}{y} \)
D). \( \Large \frac{1}{x}+\frac{1}{y} \)
5). If \( \Large \sin \theta = -\frac{4}{5}\ and\ \theta \) and \( \Large \theta \) lies in the third quadrant, then \( \Large \cos \frac{ \theta }{2} \) is equal to:
A). \( \Large \frac{1}{\sqrt{5}} \)
B). \( \Large -\frac{1}{\sqrt{5}} \)
C). \( \Large \frac{2}{\sqrt{5}} \)
D). \( \Large -\frac{2}{\sqrt{5}} \)


6). The value of \( \Large \cos 1 ^{\circ} \cos 2 ^{\circ} \cos 3 ^{\circ} ....... \cos 100 ^{\circ} \) is equal to:
A). 1
B). -1
C). 0
D). none of these
7). The value of \( \Large \sin 12 ^{\circ} \sin 48 ^{\circ} \sin 54 ^{\circ} \) is equal to:
A). \( \Large \frac{1}{16} \)
B). \( \Large \frac{1}{32} \)
C). \( \Large \frac{1}{8} \)
D). \( \Large \frac{1}{4} \)
8). The value of \( \Large 2 cos\ x - \cos 3x - \cos 5x \) is equal to
A). \( \Large 16 \cos^{3} x \sin^{2} x \)
B). \( \Large 16 \sin^{3} x \cos^{2} x \)
C). \( \Large 4 \cos^{3} x \sin^{2} x \)
D). \( \Large 4 \sin^{3} x \cos^{2} x \)
9). If \( \Large \cos \theta = \frac{1}{2} \left(x+\frac{1}{x}\right),\ then\ \frac{1}{2} \left(x^{2} + \frac{1}{x^{2}}\right) \) is equal to:
A). \( \Large \sin 2 \theta \)
B). \( \Large \sec 2 \theta \)
C). \( \Large \tan 2 \theta \)
D). \( \Large \cos 2 \theta \)
10). The value of x for the maximum value \( \Large \sqrt{3} \cos x + \sin x \) is:
A). \( \Large 30 ^{\circ} \)
B). \( \Large 45 ^{\circ} \)
C). \( \Large 60 ^{\circ} \)
D). \( \Large 90 ^{\circ} \)
Go to :
Total Pages : 4