[Note: I'm still having issues with identities with regard to trig]

Question

Verify the Trig. identities:

(a). cot(x+y)=(cotxcoty-1)/(cotx+coty)

(b). sin0(cot0+tan0)=sec0

[Note: 0=theta symbol]

Answer 1

recall that

tan(x+y) = (tanx + tany)/(1-tanx*tany)

so,

cot(x+y) = (1 - tanx tany)/(tanx + tany)

Now divide top and bottom by tanx*tany

sinx(cotx+tanx)
= sinx(cosx/sinx + sinx/cosx)
= cosx + sin^2x/cosx
= (cos^2x + sin^2x)/cosx
= secx