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If (tan θ + cot θ) = 1, sin θ + cos θ = b with 0° < θ < 90° then relation between a and b is —
- a)b2 = 2(a + b)
- b)b2 = 2(a - 1)
- c)2a = b2 - 1
- d)2a = b2 + 1
Correct answer is option 'C'. Can you explain this answer?
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If (tan θ + cot θ) = 1, sin θ + cos θ = b with...
Given Information:
- (tan θ + cot θ) = 1
- sin θ + cos θ = b
- 0° < θ="" />< />
Explanation:
Step 1: Convert tan θ and cot θ into sin θ and cos θ using trigonometric identities:
tan θ = sin θ / cos θ
cot θ = cos θ / sin θ
Step 2: Substitute the values of tan θ and cot θ in the given equation:
(sin θ / cos θ) + (cos θ / sin θ) = 1
(sin^2 θ + cos^2 θ) / (sin θ cos θ) = 1
1 / (sin θ cos θ) = 1
sin θ cos θ = 1
Step 3: Now, substitute sin θ cos θ = 1 in the second given equation:
sin θ + cos θ = b
1 / sin θ + 1 / cos θ = b
1 / sin θ + cos θ / sin θ = b
(1 + cos θ) / sin θ = b
Step 4: From the first equation, we know that 1 + cos θ = sin θ
Therefore, sin θ / sin θ = b
1 = b
Step 5: So, the relation between a and b is:
2a = b^2 - 1
Therefore, the correct answer is option 'C': 2a = b^2 - 1.
- (tan θ + cot θ) = 1
- sin θ + cos θ = b
- 0° < θ="" />< />
Explanation:
Step 1: Convert tan θ and cot θ into sin θ and cos θ using trigonometric identities:
tan θ = sin θ / cos θ
cot θ = cos θ / sin θ
Step 2: Substitute the values of tan θ and cot θ in the given equation:
(sin θ / cos θ) + (cos θ / sin θ) = 1
(sin^2 θ + cos^2 θ) / (sin θ cos θ) = 1
1 / (sin θ cos θ) = 1
sin θ cos θ = 1
Step 3: Now, substitute sin θ cos θ = 1 in the second given equation:
sin θ + cos θ = b
1 / sin θ + 1 / cos θ = b
1 / sin θ + cos θ / sin θ = b
(1 + cos θ) / sin θ = b
Step 4: From the first equation, we know that 1 + cos θ = sin θ
Therefore, sin θ / sin θ = b
1 = b
Step 5: So, the relation between a and b is:
2a = b^2 - 1
Therefore, the correct answer is option 'C': 2a = b^2 - 1.
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If (tan θ + cot θ) = 1, sin θ + cos θ = b with 0° < θ < 90° then relation between a and b is —a)b2= 2(a + b)b)b2= 2(a - 1)c)2a =b2- 1d)2a =b2+1Correct answer is option 'C'. Can you explain this answer?
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