Question

if CosecA + cotA = x then find cosecA - cotA.

Answer 1

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Answer 2

The value of $\csc A - \cot A$ is $\dfrac{1}{x}.$

Step-by-step explanation:

We have,

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

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

We know that,

$\csc^{2} A - \cot^{2} A=1$

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

[ ∵ $a^{2}-b^{2} =(a+b)(a-b)$]

⇒ $(x)(\csc A - \cot A)=1$ [Using (1)]

⇒ $\csc A - \cot A=\dfrac{1}{x}$

Hence, the value of $\csc A - \cot A$ is $\dfrac{1}{x}$.