Prove the following:
(i) cos θ tan θ = sin θ
(ii) sin θ cot θ = cos θ
(iii) sin2 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) sin2θ/cosθ + cosθ = 1/cosθ
LHS = sin2θ/cosθ + cosθ/1
Taking LCM
= (sin2θ + cos2θ)/cosθ
sin2θ + cos2θ = 1
= 1/cos θ
= RHS
Hence,
LHS = RHS.
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