# Prove that <span

To prove:

Proof:

LHS = cot θ – tan θ

But we know,

,

substituting these values in LHS, we get

But we know cos2θ + sin2θ = 1

sin2θ = 1 – cos2θ, substituting this value in the above equation, we get

= RHS

Hence proved

OR

To prove: sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + cosec θ

Proof: LHS = sin θ (1 + tan θ) + cos θ (1 + cot θ)

But we know,

,

substituting these values in LHS, we get

Now taking cos θ + sin θ common, we get

But we know cos2θ + sin2θ = 1,

substituting this value in the above equation, we get

Canceling the like terms, we get

But we know,

,

substituting these values in the above equation, we get

= cosec θ + sec θ

= RHS

Hence proved

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