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From what I know when I was teaching high school students, they tend to use the so called "Two Column Proof". In mathematics, that is not a proof and it will not be accepted in this coursel!! 1- cos 0 sin e Let me demonstrate the "Two Column Proof": Prove the identity sine 1+ cos 6 Proof: 1- cos e sin ở 1+ cos e (1 - cos e) - (1+ cos 0) = sin e - sin e 1- cos e = sin' 0 sin e = sin' e sin e Cross multiply difference of two square formula identity: sin? z + cos z = 1 The above is a standard "Two Column Proof". However, we are not trying to prove sin? e= sin 0. Therefore, this "Two Column Proof" will not be accepted in our course. Instead, we need to prove either 1) LHS (left hand side) - RHS (right hand side) or 2) LHS - an expression and RHS also equal the same expression as LHS. Here is one of the accepted proof: Proof: 1- cos e 1- cos e 1- cos e 1+ cos 0 1+ cos e sin e sin 0 LHS- sin 8 - (1+ cos 0) 1+ cos RHS sin e sin 6 sin 8 - (1+ cos 0) Please keep this in mind and try the following questions: Prove the following identities: sin e 1- cot e 1 1+ sin a= 2 seee cos e = sin 8 + cos e 1) 1- tan 8 1 1- sin e 2) 1+ sin ở 3) 1- sin e 1 =1+ tan e Hint: Some commonly used techniques includes but not limited to LCD, conjugate, convert other trigonometric function as sine and/or cosine. Generally speaking, we would begin with complicated expression.

From what I know when I was teaching high school students, they tend to use the so called "Two Column Proof". In mathematics, that is not a proof and it will not be accepted in this coursel!! 1- cos 0 sin e Let me demonstrate the "Two Column Proof": Prove the identity sine 1+ cos 6 Proof: 1- cos e sin ở 1+ cos e (1 - cos e) - (1+ cos 0) = sin e - sin e 1- cos e = sin' 0 sin e = sin' e sin e Cross multiply difference of two square formula identity: sin? z + cos z = 1 The above is a standard "Two Column Proof". However, we are not trying to prove sin? e= sin 0. Therefore, this "Two Column Proof" will not be accepted in our course. Instead, we need to prove either 1) LHS (left hand side) - RHS (right hand side) or 2) LHS - an expression and RHS also equal the same expression as LHS. Here is one of the accepted proof: Proof: 1- cos e 1- cos e 1- cos e 1+ cos 0 1+ cos e sin e sin 0 LHS- sin 8 - (1+ cos 0) 1+ cos RHS sin e sin 6 sin 8 - (1+ cos 0) Please keep this in mind and try the following questions: Prove the following identities: sin e 1- cot e 1 1+ sin a= 2 seee cos e = sin 8 + cos e 1) 1- tan 8 1 1- sin e 2) 1+ sin ở 3) 1- sin e 1 =1+ tan e Hint: Some commonly used techniques includes but not limited to LCD, conjugate, convert other trigonometric function as sine and/or cosine. Generally speaking, we would begin with complicated expression.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 72E
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From what I know when I was teaching high school students, they tend to use the so called "Two Column Proof". In mathematics, that is not a proof and it will not be accepted in this course!!! 1- cos 0 sin 8 Let me demonstrate the "Two Column Proof": Prove the identity sin 0 1+ cos e Proof: 1- cos 0 sin 0 1+ cos e sin 8 - sin 6 sin 0 (1 – cos 0) · (1 + cos 8) Cross multiply 1- cos? 0 = sin? e difference of two square formula sin? 0 = sin? 0 identity: sin? a + cos? a = 1 The above is a standard "Two Column Proof". However, we are not trying to prove sin? 0 = sin? 0. Therefore, this "Two Column Proof" will not be accepted in our course. Instead, we need to prove either 1) LHS (left hand side) = RHS (right hand side) or 2) LHS = an expression and RHS also equal the same expression as LHS. Here is one of the accepted proof: Proof: 1- cos? 0 sin 0 . (1+ cos 0) 1- cos e 1- cos 0 1+ cos 0 sin? 0 sin 0 LHS = RHS sin 0 sin 0 1+ cos e sin 0 · (1+ cos 0) 1+ cos 0 Please keep this in mind and try the following questions: Prove the following identities: cos 0 sin 0 sin 0 + cos 0 1) 1 - tan 0 1 - cot 0 1 1 2) 1- sin 0 + 1+ sin 0 = 2 sec? 0 1 = 1+ tan? 0 3) 1- sin? 0 Hint: Some commonly used techniques includes but not limited to LCD, conjugate, convert other trigonometric function as sine and/or cosine. Generally speaking, we would begin with complicated expression.
Transcribed Image Text:From what I know when I was teaching high school students, they tend to use the so called "Two Column Proof". In mathematics, that is not a proof and it will not be accepted in this course!!! 1- cos 0 sin 8 Let me demonstrate the "Two Column Proof": Prove the identity sin 0 1+ cos e Proof: 1- cos 0 sin 0 1+ cos e sin 8 - sin 6 sin 0 (1 – cos 0) · (1 + cos 8) Cross multiply 1- cos? 0 = sin? e difference of two square formula sin? 0 = sin? 0 identity: sin? a + cos? a = 1 The above is a standard "Two Column Proof". However, we are not trying to prove sin? 0 = sin? 0. Therefore, this "Two Column Proof" will not be accepted in our course. Instead, we need to prove either 1) LHS (left hand side) = RHS (right hand side) or 2) LHS = an expression and RHS also equal the same expression as LHS. Here is one of the accepted proof: Proof: 1- cos? 0 sin 0 . (1+ cos 0) 1- cos e 1- cos 0 1+ cos 0 sin? 0 sin 0 LHS = RHS sin 0 sin 0 1+ cos e sin 0 · (1+ cos 0) 1+ cos 0 Please keep this in mind and try the following questions: Prove the following identities: cos 0 sin 0 sin 0 + cos 0 1) 1 - tan 0 1 - cot 0 1 1 2) 1- sin 0 + 1+ sin 0 = 2 sec? 0 1 = 1+ tan? 0 3) 1- sin? 0 Hint: Some commonly used techniques includes but not limited to LCD, conjugate, convert other trigonometric function as sine and/or cosine. Generally speaking, we would begin with complicated expression.
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