Class 11 Mathematics · Chapter 10 · Test 4
Product-Sum Formulas
37 MCQs Covers converting products to sums and sums to products, plus proofs and special products. Also includes the objective questions I could read from the chapter self-test.
37 questions · 30 min · 37 marks
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Sample questions
The first 5 of 37. Try each one, then tap to see the answer.
Question 1
2 sin 3θ cos θ is equal to:
- Asin 4θ − sin 2θ
- Bsin 4θ + sin 2θ
- Ccos 4θ + cos 2θ
- Dcos 4θ − cos 2θ
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Answer: B
2 sin α cos β = sin(α + β) + sin(α − β), so 2 sin 3θ cos θ = sin 4θ + sin 2θ.
Question 2
2 cos 5θ sin 3θ is equal to:
- Asin 8θ + sin 2θ
- Bcos 8θ − cos 2θ
- Csin 2θ − sin 8θ
- Dsin 8θ − sin 2θ
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Answer: D
2 cos α sin β = sin(α + β) − sin(α − β), so 2 cos 5θ sin 3θ = sin 8θ − sin 2θ.
Question 3
sin 5θ cos 2θ is equal to:
- A(1/2)(sin 7θ + sin 3θ)
- B(1/2)(sin 7θ − sin 3θ)
- Csin 7θ + sin 3θ
- D(1/2)(cos 7θ + cos 3θ)
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Answer: A
sin 5θ cos 2θ = (1/2)(2 sin 5θ cos 2θ) = (1/2)[sin 7θ + sin 3θ].
Question 4
2 sin 7θ sin 2θ is equal to:
- Acos 9θ − cos 5θ
- Bcos 5θ + cos 9θ
- Ccos 5θ − cos 9θ
- Dsin 9θ − sin 5θ
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Answer: C
−2 sin α sin β = cos(α + β) − cos(α − β), so 2 sin α sin β = cos(α − β) − cos(α + β) = cos 5θ − cos 9θ.
Question 5
cos(x + y) sin(x − y) is equal to:
- A(1/2)(sin 2x + sin 2y)
- B(1/2)(sin 2x − sin 2y)
- C(1/2)(cos 2x − cos 2y)
- D(1/2)(sin 2y − sin 2x)
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Answer: B
cos A sin B = (1/2)[sin(A + B) − sin(A − B)]. With A = x + y and B = x − y: (1/2)[sin 2x − sin 2y].
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