Trigonometry SSC CGL Questions

SSC CGL-Quantitative Aptitude

Trigonometry MCQ Questions


7.
A kite is attached to a string. Find the length of the string (in m) when the height of the kite is 90 m and the string makes an angle of 30° with the ground.
SSC CGL 2021-11.04.2022-3
A.
180
B.
90√3
C.
45
D.
60√3
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ANSWER :
A. 180
8.
The value of \( 1 + \sqrt{\frac{\cot\theta + \cos\theta}{\cot\theta - \cos\theta}} \), If 0° < θ < 90°, is equal to:
SSC CGL 2021-12.04.2022-2
A.
1 - secθ + tanθ
B.
1 - secθ - tanθ
C.
1 + secθ - tanθ
D.
1 + secθ + tanθ
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ANSWER :
D. 1 + secθ + tanθ
9.
The value of \( \left(\frac{1 - \cot\theta}{1 - \tan\theta}\right)^{2} - 1 \) , When 0° < θ < 90°, is equal to:
SSC CGL 2021-12.04.2022-2
A.
cos² -1
B.
sec²θ + 1
C.
cot²θ - 1
D.
sin²θ - 1
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ANSWER :
C. cot²θ - 1
10.
If sec A = \(\dfrac{17}{8}\) given that A < 90°, what is the value of the following?
\[ \frac{34 \sin A + 15 \cot A}{68 \cos A - 16 \tan A} \]
SSC CGL 2021-11.04.2022-3
A.
23
B.
19
C.
30
D.
38
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ANSWER :
B. 19
11.
If tan²A + 2tanA - 63 = 0. Given that 0 < A < \(\dfrac{\pi}{2}\), what is the value of (2sinA + 5cosA)?
SSC CGL 2021-11.04.2022-3
A.
19√50
B.
15√50
C.
\(\dfrac{19}{\sqrt{50}}\)
D.
\(\dfrac{15}{\sqrt{50}}\)
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ANSWER :
C. \(\dfrac{19}{\sqrt{50}}\)
12.
If 3sec²θ + tanθ - 7 = 0, 0° < θ < 90°, then what is the value of \( \frac{2\sin\theta + 3\cos\theta}{\mathrm{cosec}\,\theta + \sec\theta} \) ?
SSC CGL 2021-12.04.2022-1
A.
10
B.
\(\dfrac{5}{2}\)
C.
\(\dfrac{5}{4}\)
D.
4\(\sqrt{2}\)
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ANSWER :
C. \(\dfrac{5}{4}\)