Q. 174.3( 9 Votes )

Prove that <span

Answer :

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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