Simplify the following expression

Question

cotx/cosx+1/sinx

Answer 1

1/sin(x) = csc(x)

 

cot(x) / cos(x) = cos(x)/sin(x) / cos(x) = 1/sin(x) = csc(x)

 

cot(x) / cos(x) +1/sin(x) = 2csc(x)

Answer 2

First let me make sure I'm reading your question correctly.

 

cot x            1

------   +   ------

cos x         sin x

 

Recall that cot x = cos x / sin x

With this we can restate the first term.

 

cos x / sin x             1

--------------    +   ------

    cos x                sin x

 

This reduces to

    1           1

------  +  ------

sin x       sin x

 

Which equals

 

   2

------

sin x