Question

If cosec 0 + cot 0 = x, find the value of cosec 0 - cot​

Answer 1

Hope it helps u...........

Answer 2

The value of $\csc \theta$ - $\cot \theta$ = $\dfrac{1}{x}$

Step-by-step explanation:

We have,

$\csc \theta$ + $\cot \theta$ = x                     ............ (1)

To find, the value of $\csc \theta$ - $\cot \theta$ = ?    

We know that,

The trigonometric identity,

$\csc^2 A$ - $\cot^2 A$ = 1      

Using the algebraic identity,

$a^{2} -b^{2}$ = (a + b)(a - b)

⇒ ($\csc \theta$ + $\cot \theta$)($\csc \theta$ - $\cot \theta$) = 1

Using equation (1), we get

⇒ (x)($\csc \theta$ - $\cot \theta$) = 1

⇒ $\csc \theta$ - $\cot \theta$ = $\dfrac{1}{x}$

∴ The value of $\csc \theta$ - $\cot \theta$ = $\dfrac{1}{x}$

Thus, the value of $\csc \theta$ - $\cot \theta$ is equal to $\dfrac{1}{x}$.