![\bf \textit{Sum to Product Identities} \\\\ sin(\alpha)+sin(\beta)=2sin\left(\cfrac{\alpha+\beta}{2}\right)cos\left(\cfrac{\alpha-\beta}{2}\right)\leftarrow \textit{we'll use this one} \\\\\\ sin(\alpha)-sin(\beta)=2cos\left(\cfrac{\alpha+\beta}{2}\right)sin\left(\cfrac{\alpha-\beta}{2}\right) \\\\\\ \stackrel{\textit{symmetry identity}}{cos(-\theta )=cos(\theta )} \\\\[-0.35em] \rule{34em}{0.25pt}](/tpl/images/0149/1909/ff868.png)
![\bf sin(x)+sin(3x)=\underline{4sin(x)cos^2(x)} \\\\[-0.35em] ~\dotfill\\\\ sin(x)+sin(3x)\implies 2sin\left( \cfrac{x+3x}{2} \right)cos\left( \cfrac{x-3x}{2} \right) \\\\\\ 2sin\left( \cfrac{4x}{2} \right)cos\left( \cfrac{-2x}{2} \right)\implies 2sin(2x)cos(-x)\implies 2\boxed{sin(2x)} cos(x) \\\\\\ 2\boxed{2sin(x)cos(x)} cos(x)\implies \underline{4sin(x)cos^2(x)}](/tpl/images/0149/1909/a835a.png)
Sin(x) + sin(3x) = 4 sin(x) cos^2(x)
prove the identity....
Answers: 1
Another question on Mathematics
Mathematics, 21.06.2019 17:00
Pam buys a sleeve of ball bearings for her skateboard. each of the bearings is 1 1/5 inches wide. the sleeve is 9 3/5 inches long. how many ball bearings are in the sleeve? show your work.
Answers: 3
Mathematics, 21.06.2019 20:30
Acircle has a circumference of 7.850 units. what is its radius?
Answers: 2
Mathematics, 21.06.2019 21:00
Choose the equation below that represents the line that passes through the point (2, 4) and has a slope of 3. a) y − 4 = 3(x − 2) b) y − 2 = 3(x − 4) c) y + 4 = 3(x + 2) d) y + 2 = 3(x + 4)
Answers: 1
Mathematics, 22.06.2019 00:30
Select the correct answer. employee earnings per month($) 1 1,200 2 2,600 3 1,800 4 1,450 5 3,500 6 2,800 7 12,500 8 3,200 which measure of spread is best for the data in the table? a. range b. quartiles c. interquartile range d. mean absolute deviation
Answers: 2
You know the right answer?
Questions
Social Studies, 15.07.2019 03:50
Biology, 15.07.2019 03:50
World Languages, 15.07.2019 03:50
Mathematics, 15.07.2019 03:50
History, 15.07.2019 03:50
Biology, 15.07.2019 03:50
English, 15.07.2019 03:50
English, 15.07.2019 03:50
History, 15.07.2019 03:50
Mathematics, 15.07.2019 03:50
Mathematics, 15.07.2019 03:50
Chemistry, 15.07.2019 03:50
History, 15.07.2019 03:50
