trigonometric expressions simplifying

Question

cos(x) / 1+ sin(x)  + 1+sin(x) / cos(x)

 

How do I express this as a number divided by a trigonometric function?

 

WHat i attempted was to combine the fractions and I got.

 

cos²(x)+(sin(x)+1)² / cos(x)(sin(x)+1)

 

I was thinking along the lines of expanding the numerator then you get cos²(x)+sin²(x)+1 which is 1 +1.

 

I then put my answer to be 2/  cos(x)(sin(x)+1)

 

Not sure if this is correct any help would be great

Answer 1

cosx/(1+sinx)+(1+sinx)/cosx

cos²x/(1+sinx)(cosx)+(1+sinx)(1+sinx)/(cosx)(1+sinx)

(cos²x+1+2sinx+sin²x)/(cosx)(1+sinx)

(cos²x+sin²x+1+2sinx)/(cosx)(1+sinx)

(1+1+2sinx)/(cosx)(1+sinx)

(2+2sinx)/(cosx)(1+sinx)

(2[1+sinx])/(cosx)(1+sinx)

factor out the two (1+sinx)

2/cosx  is the answer