SIMPLIFYING TRIG EXPRESSIONS USING IDENTITIES
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To simplify trigonometric identities, we have to remember the following problems.
Sometimes, we will be using the algebraic identities also to perform further simplification.
(a+b)2 = a2 + 2 ab + b2
(a-b)2 = a2 - 2 ab + b2
a2 - b2 = (a + b)(a - b)
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
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