Trigonometric ratio Questions and answers

  1. Elementary Mathematics
    1. Quadratic Equations
    2. Simplification
    3. Area and perimeter
    4. Volume and surface area
    5. Geometry
    6. Trigonometry
    7. Polynomials
    8. Height and Distance
    9. Simple and Decimal fraction
    10. Indices and Surd
    11. Logarithms
    12. Trigonometric ratio
    13. Straight lines
    14. Triangle
    15. Circles
    16. Quadrilateral and parallelogram
    17. Loci and concurrency
    18. Statistics
    19. Rectangular and Cartesian products
    20. Rational expression
    21. Set theory
    22. Factorisation
    23. LCM and HCF
    24. Clocks
    25. Real Analysis
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). \( \Large 90 ^{\circ} \)
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