Question

Find cot x if sin x cot x csc x = sqrt2

Answer 1

$\sin x\cot x\csc x=\sin x\times\dfrac{\cos x}{\sin x}\times\dfrac1{\sin x}=\cot x=\sqrt2$

Answer 2

Answer:

The value of the cotangent of x i.e. cot x is:

                              $\cot x=\sqrt{2}$

Step-by-step explanation:

We are given a trignometric equation as follows:

$\sin x\cot x\csc x=\sqrt{2}$

Now as we know that the cosecant function is the reciprocal of the sine function.

i.e. we have:

$\csc x=\dfrac{1}{\sin x}$

Hence, we solve our given expression in order to get the value of the cotangent function.

$\sin x\cot x\csc x=\sin x\csc x\cot x\\\\\sin x\cot x\csc x=\sin x\dfrac{1}{\sin x}\cot x\\\\\sin x\cot x\csc x=\cot x$

As:

$\sin x\cot x\csc x=\sqrt{2}$

                        Hence, we get that:

                          $\cot x=\sqrt{2}$