what you want to do is to show that using standard identities and algebraic manipulation, the left side can be made equal to the right side.
cosx(tanx+cotx)
change to sin,cos using trig identities
cosx(sinx/cosx + cosx/sinx)
now do some algebra
cosx*sinx/cosx + cosx*cosx/sinx
sinx + cos^2(x)/sinx
sinx*sinx/sinx + cos^2(x)/sinx
(sin^2(x) + cos^2(x))/sinx
now apply standard trig identities
1/sinx
cscx
ta-da!
I don't understand what to do after i convert everything into cos and sin.
Verify:
cosx(tanx+cotx)=cscx
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