**Prove the following:**

(i) cos θ tan θ = sin θ

(ii) sin θ cot θ = cos θ

(iii) sin^{2} θ/ cos θ + cos θ = 1/ cos θ.

**Answer :**

**(i)** cos θ tan θ = sin θ

LHS = cos θ tan θ

tan θ = sin θ/cos θ

= cos θ (sin θ/cos θ)

= 1× sin θ/1

= sin θ

= RHS

Hence, LHS = RHS.

**(ii)** sin θ cot θ = cos θ

LHS = sin θ cot θ

cot θ = cos θ/sin θ

= sin θ (cos θ/sin θ)

= 1× cos θ/1

= cos θ

= RHS

Hence, LHS = RHS.

**(iii)** sin^{2}θ/cosθ + cosθ = 1/cosθ

LHS = sin^{2}θ/cosθ + cosθ/1

Taking LCM

= (sin^{2}θ + cos^{2}θ)/cosθ

sin^{2}θ + cos^{2}θ = 1

= 1/cos θ

= RHS

Hence,

LHS = RHS.

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