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If sin θ + cos θ = 7/5, then sinθ cosθ is?
- a)11/25
- b)12/25
- c)13/25
- d)14/25
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If sin θ + cos θ = 7/5, then sinθ cosθ is?a)11...
Concept:
sin2 x + cos2 x = 1
Calculation:
Given: sin θ + cos θ = 7/5
By, squaring both sides of the above equation we get,
⇒ (sin θ + cos θ)2 = 49/25
⇒ sin2 θ + cos2 θ + 2sin θ.cos θ = 49/25
As we know that, sin2 x + cos2 x = 1
⇒ 1 + 2sin θcos θ = 49/25
⇒ 2sin θcos θ = 24/25
∴ sin θcos θ = 12/25
sin2 x + cos2 x = 1
Calculation:
Given: sin θ + cos θ = 7/5
By, squaring both sides of the above equation we get,
⇒ (sin θ + cos θ)2 = 49/25
⇒ sin2 θ + cos2 θ + 2sin θ.cos θ = 49/25
As we know that, sin2 x + cos2 x = 1
⇒ 1 + 2sin θcos θ = 49/25
⇒ 2sin θcos θ = 24/25
∴ sin θcos θ = 12/25
Most Upvoted Answer
If sin θ + cos θ = 7/5, then sinθ cosθ is?a)11...
Given Equation
Given that:
- sin(θ) + cos(θ) = 7/5
Finding sin²(θ) + cos²(θ)
We know from trigonometric identities that:
- sin²(θ) + cos²(θ) = 1
Squaring the Given Equation
Now, if we square both sides of the equation:
- (sin(θ) + cos(θ))² = (7/5)²
This expands to:
- sin²(θ) + cos²(θ) + 2sin(θ)cos(θ) = 49/25
Substituting the identity:
- 1 + 2sin(θ)cos(θ) = 49/25
Solving for sin(θ)cos(θ)
Now, let's isolate 2sin(θ)cos(θ):
- 2sin(θ)cos(θ) = 49/25 - 1
Convert 1 to a fraction:
- 1 = 25/25
Now, subtract:
- 2sin(θ)cos(θ) = 49/25 - 25/25 = 24/25
Calculating sin(θ)cos(θ)
To find sin(θ)cos(θ):
- sin(θ)cos(θ) = (24/25) / 2 = 12/25
Conclusion
Thus, the value of sin(θ)cos(θ) is:
- 12/25, matching option B.
Given that:
- sin(θ) + cos(θ) = 7/5
Finding sin²(θ) + cos²(θ)
We know from trigonometric identities that:
- sin²(θ) + cos²(θ) = 1
Squaring the Given Equation
Now, if we square both sides of the equation:
- (sin(θ) + cos(θ))² = (7/5)²
This expands to:
- sin²(θ) + cos²(θ) + 2sin(θ)cos(θ) = 49/25
Substituting the identity:
- 1 + 2sin(θ)cos(θ) = 49/25
Solving for sin(θ)cos(θ)
Now, let's isolate 2sin(θ)cos(θ):
- 2sin(θ)cos(θ) = 49/25 - 1
Convert 1 to a fraction:
- 1 = 25/25
Now, subtract:
- 2sin(θ)cos(θ) = 49/25 - 25/25 = 24/25
Calculating sin(θ)cos(θ)
To find sin(θ)cos(θ):
- sin(θ)cos(θ) = (24/25) / 2 = 12/25
Conclusion
Thus, the value of sin(θ)cos(θ) is:
- 12/25, matching option B.
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Community Answer
If sin θ + cos θ = 7/5, then sinθ cosθ is?a)11...
Concept:
sin2 x + cos2 x = 1
Calculation:
Given: sin θ + cos θ = 7/5
By, squaring both sides of the above equation we get,
⇒ (sin θ + cos θ)2 = 49/25
⇒ sin2 θ + cos2 θ + 2sin θ.cos θ = 49/25
As we know that, sin2 x + cos2 x = 1
⇒ 1 + 2sin θcos θ = 49/25
⇒ 2sin θcos θ = 24/25
∴ sin θcos θ = 12/25
sin2 x + cos2 x = 1
Calculation:
Given: sin θ + cos θ = 7/5
By, squaring both sides of the above equation we get,
⇒ (sin θ + cos θ)2 = 49/25
⇒ sin2 θ + cos2 θ + 2sin θ.cos θ = 49/25
As we know that, sin2 x + cos2 x = 1
⇒ 1 + 2sin θcos θ = 49/25
⇒ 2sin θcos θ = 24/25
∴ sin θcos θ = 12/25
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If sin θ + cos θ = 7/5, then sinθ cosθ is?a)11/25b)12/25c)13/25d)14/25Correct answer is option 'B'. Can you explain this answer?
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If sin θ + cos θ = 7/5, then sinθ cosθ is?a)11/25b)12/25c)13/25d)14/25Correct 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 If sin θ + cos θ = 7/5, then sinθ cosθ is?a)11/25b)12/25c)13/25d)14/25Correct 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 If sin θ + cos θ = 7/5, then sinθ cosθ is?a)11/25b)12/25c)13/25d)14/25Correct answer is option 'B'. Can you explain this answer?.
If sin θ + cos θ = 7/5, then sinθ cosθ is?a)11/25b)12/25c)13/25d)14/25Correct 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 If sin θ + cos θ = 7/5, then sinθ cosθ is?a)11/25b)12/25c)13/25d)14/25Correct 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 If sin θ + cos θ = 7/5, then sinθ cosθ is?a)11/25b)12/25c)13/25d)14/25Correct answer is option 'B'. Can you explain this answer?.
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