Class 11 Mathematics · Chapter 10 · Test 2
Compound Angle Identities
44 MCQs Covers exact values of 15° and 105°, the compound-angle formulas and proofs of identities. Also includes numeric problems with quadrants and the r sin(θ ± φ) form.
44 questions · 40 min · 44 marks
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Sample questions
The first 5 of 44. Try each one, then tap to see the answer.
Question 1
The exact value of sin 15° is:
- A(√3 + 1)/(2√2)
- B(√3 − 1)/(2√2)
- C(√3 − 1)/2
- D(√3 + 1)/2
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Answer: B
sin 15° = sin(45° − 30°) = sin 45° cos 30° − cos 45° sin 30° = (1/√2)(√3/2) − (1/√2)(1/2) = (√3 − 1)/(2√2).
Question 2
The exact value of cos 15° is:
- A(√3 − 1)/(2√2)
- B(√3 + 1)/2
- C(1 − √3)/(2√2)
- D(√3 + 1)/(2√2)
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Answer: D
cos 15° = cos(45° − 30°) = cos 45° cos 30° + sin 45° sin 30° = (√3 + 1)/(2√2).
Question 3
The exact value of tan 15° is:
- A2 − √3
- B2 + √3
- C√3 − 1
- D(√3 + 1)/2
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Answer: A
tan 15° = tan(45° − 30°) = (1 − 1/√3)/(1 + 1/√3) = (√3 − 1)/(√3 + 1) = 2 − √3.
Question 4
The exact value of sin 105° is:
- A(√3 − 1)/(2√2)
- B(1 − √3)/(2√2)
- C(√3 + 1)/(2√2)
- D(√3 + 1)/2
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Answer: C
sin 105° = sin(60° + 45°) = sin 60° cos 45° + cos 60° sin 45° = (√3 + 1)/(2√2).
Question 5
The exact value of cos 105° is:
- A(√3 + 1)/(2√2)
- B(1 − √3)/(2√2)
- C(√3 − 1)/(2√2)
- D(1 − √3)/2
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Answer: B
cos 105° = cos(60° + 45°) = cos 60° cos 45° − sin 60° sin 45° = (1 − √3)/(2√2), which is negative.
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