How do you simplify this expression step by step?

cot Ф

Step-by-step explanation:

Recall that sin²Ф + cos²Ф = 1, (which also says that cos²Ф - 1 = sin²Ф).

Also recall the definitions of the csc, sin and cos functions.

Your expression is equivalent to:

   1               sin Ф

 -  

sin Ф              1

           cos Ф

There are three terms in your expression:  csc, sin and cos.  Multiply all of them by sin Ф.  The result should be:

 1 - sin²Ф

sin Ф · cos Ф

Using the Pythagorean identity (see above), this simplifies to

  cos²Ф

sin Ф·cos Ф

and this whole fraction reduces to

   cos Ф

  and this ratio is the definition of the cot function.

   sin Ф

Thus, the original expression is equivalent to cot Ф

10 * 563.67 = 5636.7