SIMPLIFYING TRIG EXPRESSIONS USING IDENTITIES

Use Trigonometric Identities to write each expression in terms of a single trigonometric identity or a constant.

Problem 1 :

cot θ sin θ

Solution :

cot θ sin θ

= (cos θ/sin θ) ⋅ sin θ

= cos θ

Problem 2 :

Solution :

Problem 3 :

sin θ sec θ

Solution :

sin θ sec θ

= sin θ × (1/cos θ)

= sin θ/cos θ

= tan θ

Problem 4 :

Solution :

Problem 5 :

Solution :

Problem 6 :

Solution :

Problem 7 :

Solution :

Problem 8 :

cos θ/sec θ

Solution :

cos θ/sec θ

= cos θ/(1/cos θ)

= cos θ ⋅ cos θ

= cos²θ

Problem 9 :

Solution :

Problem 10 :

Solution :

Problem 11 :

Solution :

Problem 12 :

tan θ csc θ cos θ

Solution :

tan θ csc θ cos θ

= (sin θ/cos θ) ⋅ csc θ ⋅ cos θ

= (sin θ/cos θ) ⋅ (1/sin θ) ⋅ cos θ

= 1