Question

"Hence" means you have to use the answer from the previous answer.​

Answer 1

Step-by-step explanation:

(a) tanx=sinx/cosx

d/dx (sinx/cosx)

by u/v rule

(cosx(cosx)-sinx(-sinx))/cos²x

cos²x+sin²x/cos²x

1/cos²x

sec²(x)

1+tan²x

(b) given d/dx(tanx)=1+tan²x

d(tanx)=dx+tan²x dx

∫d(tanx) = ∫dx+∫tan²x dx

tanx= x+∫tan²x dx

∫tan²x dx=tanx-x+k

hope it helps u

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