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Suppose cos θ + sin θ = √2 cos θ, then which of the following is the correct value of cos θ - sin θ?
- a)√2 cos θ
- b)√2 sin θ
- c)-√2 cos θ
- d)-√2 sin θ
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Suppose cos θ + sin θ = √2 cos θ, then which o...
It is given that, cos θ + sin θ = √2 cos θ …..(i)
On squaring both sides, we will get,
(cos θ + sin θ)2 = (√2 cos θ)2
⇒ cos2 θ + sin2 θ + 2 sin θ cos θ = 2 cos2 θ
Or, 2cos2 θ - cos2 θ - sin2 θ = 2 sinθ cosθ
⇒ cos2 θ - sin2 θ = 2 sin θ cos θ
⇒ (cos θ + sin θ) (cos θ - sin θ) = 2 sin θ cos θ
⇒ (√2 cos θ) (cos θ - sin θ) = 2 sin θ cos θ [from equation (i)]
⇒ (cos θ - sin θ) = 2 sinθ cosθ / √2 cos θ
= √2 sin θ
On squaring both sides, we will get,
(cos θ + sin θ)2 = (√2 cos θ)2
⇒ cos2 θ + sin2 θ + 2 sin θ cos θ = 2 cos2 θ
Or, 2cos2 θ - cos2 θ - sin2 θ = 2 sinθ cosθ
⇒ cos2 θ - sin2 θ = 2 sin θ cos θ
⇒ (cos θ + sin θ) (cos θ - sin θ) = 2 sin θ cos θ
⇒ (√2 cos θ) (cos θ - sin θ) = 2 sin θ cos θ [from equation (i)]
⇒ (cos θ - sin θ) = 2 sinθ cosθ / √2 cos θ
= √2 sin θ
Most Upvoted Answer
Suppose cos θ + sin θ = √2 cos θ, then which o...
It is given that, cos θ + sin θ = √2 cos θ …..(i)
On squaring both sides, we will get,
(cos θ + sin θ)2 = (√2 cos θ)2
⇒ cos2 θ + sin2 θ + 2 sin θ cos θ = 2 cos2 θ
Or, 2cos2 θ - cos2 θ - sin2 θ = 2 sinθ cosθ
⇒ cos2 θ - sin2 θ = 2 sin θ cos θ
⇒ (cos θ + sin θ) (cos θ - sin θ) = 2 sin θ cos θ
⇒ (√2 cos θ) (cos θ - sin θ) = 2 sin θ cos θ [from equation (i)]
⇒ (cos θ - sin θ) = 2 sinθ cosθ / √2 cos θ
= √2 sin θ
On squaring both sides, we will get,
(cos θ + sin θ)2 = (√2 cos θ)2
⇒ cos2 θ + sin2 θ + 2 sin θ cos θ = 2 cos2 θ
Or, 2cos2 θ - cos2 θ - sin2 θ = 2 sinθ cosθ
⇒ cos2 θ - sin2 θ = 2 sin θ cos θ
⇒ (cos θ + sin θ) (cos θ - sin θ) = 2 sin θ cos θ
⇒ (√2 cos θ) (cos θ - sin θ) = 2 sin θ cos θ [from equation (i)]
⇒ (cos θ - sin θ) = 2 sinθ cosθ / √2 cos θ
= √2 sin θ
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Community Answer
Suppose cos θ + sin θ = √2 cos θ, then which o...
It is given that, cos θ + sin θ = √2 cos θ …..(i)
On squaring both sides, we will get,
(cos θ + sin θ)2 = (√2 cos θ)2
⇒ cos2 θ + sin2 θ + 2 sin θ cos θ = 2 cos2 θ
Or, 2cos2 θ - cos2 θ - sin2 θ = 2 sinθ cosθ
⇒ cos2 θ - sin2 θ = 2 sin θ cos θ
⇒ (cos θ + sin θ) (cos θ - sin θ) = 2 sin θ cos θ
⇒ (√2 cos θ) (cos θ - sin θ) = 2 sin θ cos θ [from equation (i)]
⇒ (cos θ - sin θ) = 2 sinθ cosθ / √2 cos θ
= √2 sin θ
On squaring both sides, we will get,
(cos θ + sin θ)2 = (√2 cos θ)2
⇒ cos2 θ + sin2 θ + 2 sin θ cos θ = 2 cos2 θ
Or, 2cos2 θ - cos2 θ - sin2 θ = 2 sinθ cosθ
⇒ cos2 θ - sin2 θ = 2 sin θ cos θ
⇒ (cos θ + sin θ) (cos θ - sin θ) = 2 sin θ cos θ
⇒ (√2 cos θ) (cos θ - sin θ) = 2 sin θ cos θ [from equation (i)]
⇒ (cos θ - sin θ) = 2 sinθ cosθ / √2 cos θ
= √2 sin θ
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Suppose cos θ + sin θ = √2 cos θ, then which of the following is the correct value of cos θ - sin θ?a)√2 cos θb)√2 sin θc)-√2 cos θd)-√2 sin θCorrect answer is option 'B'. Can you explain this answer?
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Suppose cos θ + sin θ = √2 cos θ, then which of the following is the correct value of cos θ - sin θ?a)√2 cos θb)√2 sin θc)-√2 cos θd)-√2 sin θCorrect answer is option 'B'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Suppose cos θ + sin θ = √2 cos θ, then which of the following is the correct value of cos θ - sin θ?a)√2 cos θb)√2 sin θc)-√2 cos θd)-√2 sin θCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose cos θ + sin θ = √2 cos θ, then which of the following is the correct value of cos θ - sin θ?a)√2 cos θb)√2 sin θc)-√2 cos θd)-√2 sin θCorrect answer is option 'B'. Can you explain this answer?.
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Solutions for Suppose cos θ + sin θ = √2 cos θ, then which of the following is the correct value of cos θ - sin θ?a)√2 cos θb)√2 sin θc)-√2 cos θd)-√2 sin θCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for ACT.
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Suppose cos θ + sin θ = √2 cos θ, then which of the following is the correct value of cos θ - sin θ?a)√2 cos θb)√2 sin θc)-√2 cos θd)-√2 sin θCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Suppose cos θ + sin θ = √2 cos θ, then which of the following is the correct value of cos θ - sin θ?a)√2 cos θb)√2 sin θc)-√2 cos θd)-√2 sin θCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Suppose cos θ + sin θ = √2 cos θ, then which of the following is the correct value of cos θ - sin θ?a)√2 cos θb)√2 sin θc)-√2 cos θd)-√2 sin θCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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