Trigonometry MCQs for Competitive Examination
Solve the following problems.
Q. 1
If cot 60° + cosec 60° = x, then the value of x is
(A) (1-2√2)/√2
(B) (√3-4)/2√3
(C) 1
(D) √3
Answer: (B) √3
Explanation:
Q. 2
If √[(1 – cosA)/2] = x, then the value of x is
(A) cos(A/2)
(B) tan(A/2)
(C) sin(A/2)
(D) cot(A/2)
Answer: (C) sin(A/2)
Explanation:
Q. 3
If 1 + secA = x, then the value of x is
(A) (sinAtanA)/(1 + cosA)
(B) √[sinAtanA/(1 – cosA)]
(C) (sinAtanA)/(1 – cosA)
(D) √[sinAtanA/(1 + cosA)]
Answer: (C) (sinAtanA)/(1-cosA)
Explanation:
Q. 4
If cosec -4π/3 = x, then the value of x is
(A) √2
(B) 2/√3
(C) -√2
(D) -1/√3
Answer: (B) (2/√3)
Explanation:
Q. 5
If cot(A/2) = x, then the value of x is
(A) √[(1 + cosA)/(1 – cosA)]
(B) cosecA – cotA
(C) √[(1 – cosA)/2]
(D) √[(1 + cosA) /2]
Answer: (A) √[(1+cosA)/(1-cosA)]
Explanation:
Q. 6
If (1 – cosA) /(1 + cosA) = x, then the value of x is
(A) (cotA + cosecA)2
(B) (cotA – cosecA) 2
(C) cotA – cosecA
(D) cotA + cosecA
Answer: (B) (cotA-cosecA)²
Explanation:
Q. 7
If sec -7π/4 = x, then the value of x is
(A) √2
(B) -√2
(C) -1/√3
(D) -1
Answer: (A) √2
Explanation:
Q. 8
If tan(A/2) = x, then the value of x is
(A) (1 – cosA)/sinA
(B) (1 + cosA)/sinA
(C) √[(1 – cosA)/sinA]
(D) √[(1 + cosA)/sinA]
Answer: (A) (1-cosA)/sinA
Explanation:
Q. 9
If (secA – tanA)2 = x, then the value of x is
(A) (1 + sinA)/(1 – sinA)
(B) √[(1 – sinA)/(1 + sinA)]
(C) (1 – sinA)/(1 + sinA)
(D) √[(1 + sinA)/(1 – sinA)]
Answer: (A) (1+sinA)/(1-sinA)
Explanation:
Q. 10
What is the value of sin 5π/3?
(A) √3/2
(B) 2/√3
(C) 1/√3
(D) -2/√3
Answer: (A) Rs √3/2
Explanation:
Q. 11
cos3A is equal to
(A) cos3A – 3sin2cosA
(B) cos3A + 4sin2cosA
(C) cos3A + 3sin2cosA
(D) cos3A – 4sin2cosA
Answer: (D) Rs 600
Explanation:
Q. 12
2 sec2A is equal to
(A) (1 – tanA)2 – (1 + tanA)2
(B) √[(1 – tanA)2 + (1 + tanA)2]
(C) √[(1 – tanA)2 – (1 + tanA)2]
(D) (1 – tanA)2 + (1 + tanA)2
Answer: (D) (1 – tanA)2 + (1 + tanA)2
Explanation;
Q. 13
What is the value of cosec 11π/6?
(A) -2/√3
(B) √2
(C) -2
(D) -√2
Answer: (C) -2
Explanation:
Q. 14
1/(tanA + cotA) is equal to
(A) (cosecA + sinA)(secA – cosA)
(B) √[(cosecA – sinA)(secA – cosA)]
(C) √[(cosecA + sinA)(secA – cosA)]
(D) (cosecA – sinA)(secA – cosA)
Answer: (D) (cosecA-sinA)(secA-cosA)
Explanation:
Q. 15
If cosAcotA/(1 sinA) = x, then the value of x is
(A) 1 -cosecA
(B) 1 + cosecA
(C) 1 + secA
(D) 1/secA
Answer: (B) 1+cosecA
Explanation:
Q. 16
sin(A+B) – sin(A-B) is equal to
(A) 2sinAcosB
(B) 2cosAcosB
(C) 2cosAsinB
(D) 2sinAsinB
Answer: (C) 2cosAsinB
Explanation:
Q. 17
2 – (cosA + sinA)2 is equal to
(A) (cosecA – sinA)2
(B) cosA – sinA
(C) cosecA – sinA
(D) (cosA – sinA)2
Answer: (D) (cosA – sinA)2
Explanation:
Q. 18
The value of (sec245 – cot245) – (sin230 + sin260) is
(A) 1
(B) 2√3
(C) 0
(D) 1/√2
Answer: (C) 0
Explanation:
Q. 19
cot2Acos2A is equal to
(A) cot2A + cos2A
(B) tan2A – cos2A
(C) cot2A – cos2A
(D) tan2A + cos2A
Answer: (C) cot2A – cos2A
Explanation:
Q. 20
tan2Asin2A is equal to
(A) tan2A – sin2A
(B) tan2A + sin2A
(C) cot2A – sin2A
(D) cot2A + sin2A
Answer: (A) cot2A + sin2A
Explanation: