If (\cosec x+\cot x=6), what is the value of (\cosec x-\cot x)?
Answer and explanation
Correct answer: (\frac{1}{6}) / (\frac{1}{6}
The two expressions involving cosecant and cotangent are connected by a standard identity. Since \\(\cosec^2 x-\cot^2 x=1\\), their product can be written as \\(\bigl(\cosec x+\cot x\bigr)\bigl(\cosec x-\cot x\bigr)=1\\). This identity is valid wherever the expressions are defined, so it directly links the given sum with the required difference.
The given sum is \\(\cosec x+\cot x=6\\). Substituting this into the product identity gives \\(6(\cosec x-\cot x)=1\\). Dividing both sides by 6, we obtain \\(\cosec x-\cot x=\frac{1}{6}\\). Therefore, option A is correct. The answer is not 6 because the second factor must be the reciprocal of the first factor.
Frequently asked questions
What is the correct answer to this question?
(\frac{1}{6}) / (\frac{1}{6}
Why is this the correct answer?
The two expressions involving cosecant and cotangent are connected by a standard identity. Since \\(\cosec^2 x-\cot^2 x=1\\), their product can be written as \\(\bigl(\cosec x+\cot x\bigr)\bigl(\cosec x-\cot x\bigr)=1\\). This identity is valid wherever the expressions are defined, so it directly links the given sum with the required difference.
The given sum is \\(\cosec x+\cot x=6\\). Substituting this into the product identity gives \\(6(\cosec x-\cot x)=1\\). Dividing both sides by 6, we obtain \\(\cosec x-\cot x=\frac{1}{6}\\). Therefore, option A is correct. The answer is not 6 because the second factor must be the reciprocal of the first factor.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
