TRIGONOMETRY - Quotient Identities

Quotient Identities in Trigonometry :

Solved Problems

Prove each of the following :

Problem 1 :

tan θ ⋅ cos θ = sin θ

Solution :

= tan θ ⋅ cos θ

Problem 2 :

cot θ ⋅ sin θ = cos θ

Solution :

= cot θ ⋅ sin θ

Problem 3 :

tan θ ⋅ csc θ = 1

Solution :

= tan θ ⋅ sec θ

Problem 4 :

Solution :

Problem 5 :

Solution :

Problem 6 :

Solution :

Problem 7 :

Solution :

Problem 8 :

Solution :

Problem 9 :

tan2θ sin2θ = tan2θ - sin2 θ

Solution :

= tan2θ sin2θ

= (sec2θ - 1)sin2θ

= sec2θ sin2θ - sin2θ

Problem 10 :

Solution :

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