TRIGONOMETRY - Quotient Identities

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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