Question

Verify the Identity:
csc(x)+sec(x)/sin(x)+cos(x)=cot(x)+tan(x)

the left side of the equation is all one term.

Answer 1

Verify:
(csc(x)+sec(x))/(sin(x)+cos(x))=cot(x)+tan(x)

Left hand side
(csc(x)+sec(x))/(sin(x)+cos(x))
=(1/sin(x)+1/(cos(x))/(sin(x)+cos(x))
=((cos(x)+sin(x))/(sin(x)cos(x))/(sin(x)+cos(x))
=1/(sin(x)cos(x))

Right hand side:
cot(x)+tan(x)
=cos(x)/sin(x) + sin(x)/cos(x)
=(cos²(x) + sin²(x))/(sin(x)+cos(x))
=1/(sin(x)+cos(x))

So the identity is verified.