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If sin θ + sin 2θ + sin 3θ = sin α and cos θ + cos 2θ + cos 3θ = cos α , then θ is equal to
- a)α/2
- b)α
- c)2α
- d)α/6
Correct answer is option 'A'. Can you explain this answer?
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If sin θ + sin 2θ + sin 3θ = sin α and cos &th...
sinθ+sin3θ+sin2θ=sinα
⇒ 2 sin 2θ cosθ + sin 2θ = sin α
⇒ 2 sin 2θ cosθ + sin 2θ = sin α
⇒ sin 2θ(2 cos θ +1) = sin α........(1)
Now cos θ + cos 3θ + cos 2θ = cos α cos 2θ (2 cos θ + 1) = cos α. ....(2)
From (1) and (2), tan 2θ = tan α ⇒ 2θ = α ⇒θ = α/2
Now cos θ + cos 3θ + cos 2θ = cos α cos 2θ (2 cos θ + 1) = cos α. ....(2)
From (1) and (2), tan 2θ = tan α ⇒ 2θ = α ⇒θ = α/2
Most Upvoted Answer
If sin θ + sin 2θ + sin 3θ = sin α and cos &th...
sinθ+sin3θ+sin2θ=sinα
⇒ 2 sin 2θ cosθ + sin 2θ = sin α
⇒ 2 sin 2θ cosθ + sin 2θ = sin α
⇒ sin 2θ(2 cos θ +1) = sin α........(1)
Now cos θ + cos 3θ + cos 2θ = cos α cos 2θ (2 cos θ + 1) = cos α. ....(2)
From (1) and (2), tan 2θ = tan α ⇒ 2θ = α ⇒θ = α/2
Now cos θ + cos 3θ + cos 2θ = cos α cos 2θ (2 cos θ + 1) = cos α. ....(2)
From (1) and (2), tan 2θ = tan α ⇒ 2θ = α ⇒θ = α/2
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If sin θ + sin 2θ + sin 3θ = sin α and cos &th...
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If sin θ + sin 2θ + sin 3θ = sin α and cos θ + cos 2θ + cos 3θ = cos α , then θ is equal toa)α/2b)αc)2αd)α/6Correct answer is option 'A'. Can you explain this answer?
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