Question

sin[sin3+sin5]=cos[cos3-cos5]
Establish the identity
I used the sum to product formula so far

Answer 1

is that a literal 3 and 5? or are those exponents?

Answer 2

that is \(\bf \large sin[sin(3)+sin(5)]=cos[cos(3)-cos(5)] ?\)

Answer 3

yes it's just three and five, they have thetas after them as well @jdoe0001

Answer 4

hmmm

Answer 5

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJzaW4oc2luKDN4KStzaW4oNXgpKSIsImNvbG9yIjoiI0QxMUYxRiJ9LHsidHlwZSI6MCwiZXEiOiJjb3MoY29zKDN4KS1jb3MoNXgpKSIsImNvbG9yIjoiIzE4MzlERSJ9LHsidHlwZSI6MTAwMCwid2luZG93IjpbIi02LjUxOTk5OTk5OTk5OTk5OSIsIjYuNDgiLCItMy45OCIsIjQuMDIiXX1d


hmmmm.....so... as you can see. hmmm
I tried a few dead ends ...so....notice the graph

Answer 6

I have to show how the left side equals the right without changing the right hand side

Answer 7

Using trig functions

Answer 8

well... if you notice the graph
you'd end up in dead ends though

Answer 9

Is this what you are trying to show?\[\sin(\theta)\left(\sin(3\theta)+\sin(5\theta)\right)=\cos(\theta)\left(\cos(3\theta)-\cos(5\theta)\right)\]

Answer 10

Yes

Answer 11

OK - notice how in this identity we have \(\theta,3\theta,5\theta\) where we notice that:\[\theta+3\theta=4\theta\]and:\[5\theta-\theta=4\theta\]

Answer 12

Can you see how to make use of this fact?

Answer 13

Think about the cosine addition and subtraction formulas

Answer 14

I tried using the sum to product formula

Answer 15

From what I showed you above we can write:\[\theta+3\theta=5\theta-\theta\]Now just take cosines of both sides to get:\[\cos(\theta+3\theta)=\cos(5\theta-\theta)\]
Finally expand each of these using the cosine addition/subtraction formulas, rearrange and you will get to the desired identity.

Answer 16

I dont understand how you got that in the previous part @asnaseer

Answer 17

1+3=5-1=4

Answer 18

Do you understand?

Answer 19

Isnt the sin on the outside multiplied

Answer 20

Yes it is, and if you expand this out as I suggested then you will get to your identity:\[\cos(\theta+3\theta)=\cos(5\theta-\theta)\]

Answer 21

Have you been asked to specifically use the sum to product formulas?