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Question (21)

QN0036841

21. If tan A = 1, then sin A cos A equals:

(A) 1
(B) 1/2
(C) 1/4
(D) √2/2

Correct Answer: B

Explanation:

A = 45°, so sin A = cos A = 1/√2. Their product is 1/2.

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Question (22)

QN0036842

22. If cot A = 1, then sec²A + cosec²A is:

(A) 2
(B) 3
(C) 4
(D) 5

Correct Answer: C

Explanation:

A = 45°. Therefore sec²45° = 2 and cosec²45° = 2. Their sum is 4.

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Question (23)

QN0036843

23. If sin A = 1/2 and A is acute, then tan A is:

(A) 1/√3
(B) √3
(C) 1
(D) 1/2

Correct Answer: A

Explanation:

A = 30°, hence tan 30° = 1/√3.

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Question (24)

QN0036844

24. If cos A = 1/2 and A is acute, then cosec A equals:

(A) 1
(B) 2
(C) 2/√3
(D) √3

Correct Answer: C

Explanation:

A = 60°. Therefore sin 60° = √3/2 and cosec 60° = 2/√3.

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Question (25)

QN0036845

25. The value of sin 60° cos 30° + cos 60° sin 30° is:

(A) 0
(B) 1/2
(C) 1
(D) √3/2

Correct Answer: C

Explanation:

(√3/2)(√3/2) + (1/2)(1/2) = 3/4 + 1/4 = 1.

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Question (26)

QN0036846

26. The value of cos²30° + cos²60° is:

(A) 1/2
(B) 1
(C) 3/2
(D) 2

Correct Answer: B

Explanation:

cos²30° = 3/4 and cos²60° = 1/4. Their sum is 1.

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Question (27)

QN0036847

27. The value of tan 30° tan 60° is:

(A) 1/3
(B) 1
(C) √3
(D) 3

Correct Answer: B

Explanation:

tan 30° tan 60° = (1/√3)(√3) = 1.

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Question (28)

QN0036848

28. The value of sec 60° − cos 60° is:

(A) 1/2
(B) 3/2
(C) 5/2
(D) 1

Correct Answer: B

Explanation:

sec 60° = 2 and cos 60° = 1/2. Hence the difference is 3/2.

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Question (29)

QN0036849

29. The value of cosec 30° − sec 60° is:

(A) 0
(B) 1
(C) 2
(D) 1/2

Correct Answer: A

Explanation:

cosec 30° = 2 and sec 60° = 2. Therefore, the difference is 0.

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Question (30)

QN0036850

30. The value of sin 60°/cos 30° is:

(A) 1/2
(B) 1
(C) √3
(D) 2

Correct Answer: B

Explanation:

sin 60° and cos 30° are both √3/2, so their ratio is 1.

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Question (21)

21. If tan A = 1, then sin A cos A equals:

Explanation:

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Question (22)

22. If cot A = 1, then sec²A + cosec²A is:

Explanation:

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Question (23)

23. If sin A = 1/2 and A is acute, then tan A is:

Explanation:

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Question (24)

24. If cos A = 1/2 and A is acute, then cosec A equals:

Explanation:

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Question (25)

25. The value of sin 60° cos 30° + cos 60° sin 30° is:

Explanation:

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Question (26)

26. The value of cos²30° + cos²60° is:

Explanation:

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Question (27)

27. The value of tan 30° tan 60° is:

Explanation:

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Question (28)

28. The value of sec 60° − cos 60° is:

Explanation:

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Question (29)

29. The value of cosec 30° − sec 60° is:

Explanation:

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Question (30)

30. The value of sin 60°/cos 30° is:

Explanation:

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