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If tan θ - cot θ = 0, what will be the value of sin θ + cos θ?
- a)1
- b)√2
- c)1/√2
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If tan θ - cot θ = 0, what will be the value of sin &theta...
Given tan θ - cot θ = 0
Let's put θ = 450 in order to satisfy the above equation
tan 450 - cot 450 = 0
1 - 1 = 0 (equation satisfied with θ = 450)
Now, put θ = 450 in sin θ + cos θ, we will get
= sin 450 + cos 450
= 1/√2 + 1/√2
= √2
Let's put θ = 450 in order to satisfy the above equation
tan 450 - cot 450 = 0
1 - 1 = 0 (equation satisfied with θ = 450)
Now, put θ = 450 in sin θ + cos θ, we will get
= sin 450 + cos 450
= 1/√2 + 1/√2
= √2
Most Upvoted Answer
If tan θ - cot θ = 0, what will be the value of sin &theta...
Given tan θ - cot θ = 0
Let's put θ = 450 in order to satisfy the above equation
tan 450 - cot 450 = 0
1 - 1 = 0 (equation satisfied with θ = 450)
Now, put θ = 450 in sin θ + cos θ, we will get
= sin 450 + cos 450
= 1/√2 + 1/√2
= √2
Let's put θ = 450 in order to satisfy the above equation
tan 450 - cot 450 = 0
1 - 1 = 0 (equation satisfied with θ = 450)
Now, put θ = 450 in sin θ + cos θ, we will get
= sin 450 + cos 450
= 1/√2 + 1/√2
= √2
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Community Answer
If tan θ - cot θ = 0, what will be the value of sin &theta...
Understanding the Equation
When tan θ - cot θ = 0, it implies that:
- tan θ = cot θ
We know that:
- tan θ = sin θ / cos θ
- cot θ = cos θ / sin θ
Setting these equal gives:
- sin θ / cos θ = cos θ / sin θ
Cross Multiplying
Cross multiplying leads to:
- sin² θ = cos² θ
This can be rewritten using the Pythagorean identity:
- sin² θ + cos² θ = 1
Finding the Values of sin θ and cos θ
From sin² θ = cos² θ, we can infer:
- sin² θ = 1/2
- cos² θ = 1/2
Thus, we have:
- sin θ = ± 1/√2
- cos θ = ± 1/√2
Calculating sin θ + cos θ
Now, we need to find:
- sin θ + cos θ = ± 1/√2 ± 1/√2
Considering both positive values, we get:
- sin θ + cos θ = 1/√2 + 1/√2 = 2/√2 = √2
Conclusion
Hence, the value of sin θ + cos θ is:
- √2
Thus, the correct answer is option 'B'.
When tan θ - cot θ = 0, it implies that:
- tan θ = cot θ
We know that:
- tan θ = sin θ / cos θ
- cot θ = cos θ / sin θ
Setting these equal gives:
- sin θ / cos θ = cos θ / sin θ
Cross Multiplying
Cross multiplying leads to:
- sin² θ = cos² θ
This can be rewritten using the Pythagorean identity:
- sin² θ + cos² θ = 1
Finding the Values of sin θ and cos θ
From sin² θ = cos² θ, we can infer:
- sin² θ = 1/2
- cos² θ = 1/2
Thus, we have:
- sin θ = ± 1/√2
- cos θ = ± 1/√2
Calculating sin θ + cos θ
Now, we need to find:
- sin θ + cos θ = ± 1/√2 ± 1/√2
Considering both positive values, we get:
- sin θ + cos θ = 1/√2 + 1/√2 = 2/√2 = √2
Conclusion
Hence, the value of sin θ + cos θ is:
- √2
Thus, the correct answer is option 'B'.
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