Question

if cosecQ + cotQ= x, then find the value of cosecQ - cotQ.

Answer 1

Step-by-step explanation:

see the adjoining attachment..

This is your answer.........

Answer 2

Answer:

$\\ (\csc(Q) - \cot(Q)) \: = \frac{1}{x}$

Step-by-step explanation:

Given :

cosecQ + cotQ = x

To Find : cosecQ - cotQ

Solution:

$\\ \\ \csc(Q) + \cot(Q) = x \\ \\ but \: \: we \: \: know \: that \: \\ \\ \\ { (\csc(Q)) }^{2} - { (\cot(Q)) }^{2} = 1 \\ \\ \\ but \: {a}^{2} - {b}^{2} = (a + b)(a - b)$

So, we get;

$\\ ( \csc(Q) + \cot(Q) )( \csc(Q) - \cot(Q) ) = 1 \\ \\ putting \: \: given \: value \: \\ \\ \\ x \: \times (\csc(Q) - \cot(Q)) = 1 \\ \\ so \: \: (\csc(Q) - \cot(Q)) \: = \: \frac{1}{x}$

Thanks.