Q17 of 30 Page 1

Prove that

OR


Prove that: sin θ (1 + tan θ) + cos θ (1 + cot θ) = sec θ + cosec θ


To prove:


Explanation:


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 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 above equation, we get





Cancelling the like terms, we get



But we know ,


substituting these values in above equation, we get


= cosec θ + sec θ


= RHS


Hence proved


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