Quotient Identities in Trigonometry :
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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