Question

If cosec x + cot x = x, find the value of cosec x - cot x.

(A) 1/x
(B) x
(C) 1 - x
(D) x^2 - 1

Answer 1

To find the value of cosec x - cot x given cosec x + cot x = x, we can use trigonometric identities. Simplifying the equation and expressing cosec x - cot x in terms of sine and cosine, the value is found to be 1/x. Hence the correct answer is option A

Step-by-step explanation:

To find the value of cosec x - cot x given cosec x + cot x = x, we can use trigonometric identities. Let's start by expressing cosec x and cot x in terms of sine and cosine:

1. cosec x = 1/sin x
2. cot x = cos x/sin x

Now, substitute these values into the given equation:

1/sin x + cos x/sin x = x

Simplify the equation:

(1 + cos x)/sin x = x

Now, we can express cosec x - cot x in terms of sine and cosine:

cosec x - cot x = 1/sin x - cos x/sin x = (1 - cos x)/sin x

Since we know that (1 + cos x)/sin x = x, we can substitute this value:

cosec x - cot x = (1 - cos x)/sin x = (1 - (1 + cos x))/sin x = 1/sin x = 1/x

Hence the correct answer is option A