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C3 Proofs
The few proofs which need learnt for C3
4
Mathematics
Intermediate
05/17/2016
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Term
Prove that y=lnx dy/dx= 1/x
 Definition

y=lnx

ey=x

dx/dy=ey

dy/dx =1/ey

now, y=lnx

∴ dy/dx= 1/elnx

=1/x
Term

Prove that Cosec2θ = 1+Cot2θ

 

 

 Definition

Sin2θ+Cos2θ= 1

(Sin2θ/Sin2θ)+(Cos2θ/Sin2θ) = (1/Sin2θ)

1+ (Cosθ/Sinθ)2 =(1/Sinθ)2

1+Cot2θ = Cosec2θ
Term
Prove that Sec2θ=1+Tan2θ
 Definition

Sin2θ+Cos2θ= 1

Sin2θ/Cos2θ)+(Cos2θ/Cos2θ) = (1/Cos2θ)

(Sinθ/Cosθ)2 +1= (1/Cosθ)2

Sec2θ=1+Tan2θ
Term
Prove that Cotθ =Cosθ/Sinθ
 Definition

Tanθ= Sinθ/Cosθ

Cotθ=1/Tanθ

1/Tanθ=Cosθ/Sinθ

Cotθ= Cosθ/Sinθ
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