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Simplification
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Question
What is the value of [2 cot × (p ? A)/2]/[1 + tan2× (2p ? A)/2] ?
Options
A. 2 sin2 A/2
B. cos A
C. sin A
D. 2 cos2 A/2
Correct Answer
sin A
Tags:
Bank Exams
Simplification problems
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1. What is the value of (32 cos6x ? 48 cos4x + 18 cos2x ? 1)/[4 sin x cos x sin (60 ? x) cos (60 ? x) sin (60 + x) cos (60 + x)] ?
Options
A. 4 tan 6x
B. 4 cot 6x
C. 8 cot 6x
D. 8 tan 6x
Show Answer
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Correct Answer: 8 cot 6x
2. What is the value of {(sin 4x + sin 4y) [(tan 2x ? 2y)]}/(sin 4x ? sin 4y)?
Options
A. tan 2 (2x + 2y)
B. tan2
C. cot (x ? y)
D. tan (2x + 2y)
Show Answer
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Correct Answer: tan (2x + 2y)
3. Triangle PQR is inscribed in a circle such that P, Q and R lie on the circumference. If PQ is the diameter of the circle and ?PQR = 40°, then what is the value (in degrees) of ?QPR?
Options
A. 40
B. 45
C. 50
D. 55
Show Answer
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Correct Answer: 50
4. PAB and PCD are two secants to a circle. If PA = 10 cm, AB = 12 cm and PC = 11 cm, then what is the value (in cm) of PD?
Options
A. 18
B. 9
C. 20
D. 12
Show Answer
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Correct Answer: 20
5. PQR is an equilateral triangle whose side is 10 cm. What is the value (in cm) of the inradius of triangle PQR?
Options
A. 5/?3
B. 10?3
C. 10/?3
D. 5?2
Show Answer
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Correct Answer: 5/?3
6. If tan ? + sec ? = (x ? 2)/(x + 2), then what is the value of cos ??
Options
A. (x2 ? 1)/(x2 + 1)
B. (2x2 ? 4)/(2x2 + 4)
C. (x2 ? 4)/(x2 + 4)
D. (x2 ? 2)/(x2 + 2)
Show Answer
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Correct Answer: (x2 ? 4)/(x2 + 4)
7. What is the value of (cos 40° ? cos 140°)/(sin 80° + sin 20°)?
Options
A. 2?3
B. 2/?3
C. 1/?3
D. ?3
Show Answer
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Correct Answer: 2/?3
8. What is the value of [1 ? tan (90 ? ?) + sec (90 ? ?)]/[tan (90 ? ?) + sec (90 ? ?) + 1]?
Options
A. cot (?/2)
B. tan (?/2)
C. sin ?
D. cos ?
Show Answer
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Discuss
Correct Answer: tan (?/2)
9. What is the value of [sin (90 ? A) + cos (180 ? 2A)]/[cos (90 ? 2A) + sin (180 ? A)]?
Options
A. sin (A/2) cos A
B. cot (A/2)
C. tan (A/2)
D. sin A cos (A/2)
Show Answer
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Discuss
Correct Answer: tan (A/2)
10. If P = 22 + 62 + 102 + 142 + ... 942 and Q = 12 + 52 + 92 + ... 812 , then what is the value of P ? Q?
Options
A. 24645
B. 26075
C. 29317
D. 31515
Show Answer
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Correct Answer: 26075
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