This is a "proving of identities" problem
(cos x+cot x)sec x=1 +cosec x
(cosx + cosx/sinx)/cosx = 1 + 1/sinx
cosx + cosx/sinx = cosx + cosx/sinx
0 = 0
QED
(cos x+cot x)sec x
=(cosx+cosx/sinx)/cosx
= 1+1/sinx
=1+cosec(x) QED
cos(1+cosec)sec=1+cosec
Comments
(cos x+cot x)sec x=1 +cosec x
(cosx + cosx/sinx)/cosx = 1 + 1/sinx
cosx + cosx/sinx = cosx + cosx/sinx
0 = 0
QED
(cos x+cot x)sec x
=(cosx+cosx/sinx)/cosx
= 1+1/sinx
=1+cosec(x) QED
cos(1+cosec)sec=1+cosec