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Question (41)

QN0036861

41. If tan A = 3/4, then (1 − tan²A)/(1 + tan²A) is:

(A) 7/25
(B) 7/16
(C) 9/25
(D) 16/25

Correct Answer: A

Explanation:

(1 − 9/16)/(1 + 9/16) = (7/16)/(25/16) = 7/25.

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Question (42)

QN0036862

42. If cot A = 4/3, then sin A is:

(A) 3/5
(B) 4/5
(C) 3/4
(D) 5/4

Correct Answer: A

Explanation:

Adjacent:opposite = 4:3, giving a 3-4-5 triangle. Hence sin A = 3/5.

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Question (43)

QN0036863

43. If sec A = 5/4, then sec²A − tan²A is:

(A) 0
(B) 1
(C) 9/16
(D) 7/16

Correct Answer: B

Explanation:

Using sec²A = 1 + tan²A, sec²A − tan²A = 1.

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Question (44)

QN0036864

44. If cosec A = 13/5, then cosec²A − cot²A equals:

(A) 0
(B) 1
(C) 25/169
(D) 144/169

Correct Answer: B

Explanation:

Using cosec²A = 1 + cot²A, the difference is 1.

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Question (45)

QN0036865

45. If tan A = 2/3, then sin A/cos A + cos A/sin A is:

(A) 13/6
(B) 5/6
(C) 12/13
(D) 13/12

Correct Answer: A

Explanation:

sin A/cos A = tan A = 2/3 and cos A/sin A = cot A = 3/2. Therefore, the sum is 2/3 + 3/2 = 13/6.

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Question (46)

QN0036866

46. If sin A = 12/13, then tan A/sec A is:

(A) 5/13
(B) 12/13
(C) 5/12
(D) 12/5

Correct Answer: B

Explanation:

tan A/sec A = (sin A/cos A)/(1/cos A) = sin A = 12/13.

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Question (47)

QN0036867

47. If A + B = 90° and tan A = 3/4, then tan B is:

(A) 3/4
(B) 4/3
(C) 7/25
(D) 25/7

Correct Answer: B

Explanation:

Since B = 90° − A, tan B = cot A = 4/3.

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Question (48)

QN0036868

48. If A + B = 90°, A > B, and sin A = √3/2, then B is:

(A) 15°
(B) 30°
(C) 45°
(D) 60°

Correct Answer: B

Explanation:

sin A = √3/2 gives A = 60°. Therefore, B = 90° − 60° = 30°.

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Question (49)

QN0036869

49. For an acute angle A, which expression has the value 1?

(A) sec A − tan A
(B) sec²A − tan²A
(C) cosec A − cot A
(D) tan A − cot A

Correct Answer: B

Explanation:

From the identity sec²A = 1 + tan²A, we get sec²A − tan²A = 1.

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Question (50)

QN0036870

50. If tan A = 3/4, then the value of sin²A + cos²A + tan²A is:

(A) 16/9
(B) 25/16
(C) 25/9
(D) 2

Correct Answer: B

Explanation:

Since sin²A + cos²A = 1, the expression is 1 + tan²A = 1 + 9/16 = 25/16.

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Question (41)

41. If tan A = 3/4, then (1 − tan²A)/(1 + tan²A) is:

Explanation:

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Question (42)

42. If cot A = 4/3, then sin A is:

Explanation:

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Question (43)

43. If sec A = 5/4, then sec²A − tan²A is:

Explanation:

Link:

Question (44)

44. If cosec A = 13/5, then cosec²A − cot²A equals:

Explanation:

Link:

Question (45)

45. If tan A = 2/3, then sin A/cos A + cos A/sin A is:

Explanation:

Link:

Question (46)

46. If sin A = 12/13, then tan A/sec A is:

Explanation:

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Question (47)

47. If A + B = 90° and tan A = 3/4, then tan B is:

Explanation:

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Question (48)

48. If A + B = 90°, A > B, and sin A = √3/2, then B is:

Explanation:

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Question (49)

49. For an acute angle A, which expression has the value 1?

Explanation:

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Question (50)

50. If tan A = 3/4, then the value of sin²A + cos²A + tan²A is:

Explanation:

Link:

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