simplifying trigonometric equation using identities,

sin(A+B)≡sin(A)cos(B)+cos(A)sin(B)

sin(A-B)≡sin(A)cos(B)-cos(A)sin(B)

sin(A+B)+sin(A-B)≡2sin(A)cos(B)

Let A+B=4x and A-B=2x, then A=3x and B=x, so sin(4x)+sin(2x)≡2sin(3x)cos(x).

sin(6x)≡2sin(3x)cos(3x).

sin(2x)+sin(4x)-sin(6x)≡

2sin(3x)cos(x)-2sin(3x)cos(3x)=

2sin(3x)(cos(x)-cos(3x)).

cos(A+B)≡cos(A)cos(B)-sin(A)sin(B)

cos(A-B)≡cos(A)cos(B)+sin(A)sin(B)

cos(A-B)-cos(A+B)≡2sin(A)sin(B).

Let A-B=x and A+B=3x, then A=2x and B=x, so cos(x)-cos(3x)≡2sin(2x)sin(x).

Therefore:

2sin(3x)(cos(x)-cos(3x))≡

sin(2x)+sin(4x)-sin(6x)≡

(2sin(3x))(2sin(2x)sin(x))=

4sin(x)sin(2x)sin(3x) QED

- All categories
- Pre-Algebra Answers 12.3k
- Algebra 1 Answers 25.3k
- Algebra 2 Answers 10.5k
- Geometry Answers 5.2k
- Trigonometry Answers 2.6k
- Calculus Answers 6.1k
- Statistics Answers 3k
- Word Problem Answers 10.2k
- Other Math Topics 6.7k

81,952 questions

86,346 answers

2,238 comments

71,629 users