Tanx(sinx+cotx cosx) to secx How do I do this???

Question

I am working with Identites. I'm surpose to go from Tanx(sinx+ cotx cosx) and get to secx.

Answer 1

tan ( sin + cot cos ) = sec

(sin/cos) (sin + (cos/sin)(cos)) = sec

sin² /cos + cos = sec

(sin² + cos²) / cos = sec

1/ cos = sec

sec = sec