Question

Use the sum-to-product formulas to find the exact value of the expression.
5 sin 75° + 5 sin 15°

Answer 1

May I help?

Answer 2

Yes, please!

Answer 3

Yes, please! @3mar

Answer 4

I plugged it into the formula but got the wrong answer

Answer 5

Of course.
With my pleasure!

So why you don't use angles (45) and (30) with their addition and subtraction to form the the angles (75) and (15)?

Answer 6

2*5 Sin ( (75°+15°)/2) cos( (75°-15°)/2)

Answer 7

10Sin (45°) Cos(30°)

Answer 8

That was my final answer but it was marked wrong

Answer 9

Why /2?
\(2*5 Sin ( (75°+15°)\color{red}{/2}) cos( (75°-15°)\color{red}{/2})\)

Answer 10

Yes! Two is part of the formula so I divided it into the final answer

Answer 11

No sister!

How did you get that\(10Sin (45°) Cos(30°)\) form this \(2*5 Sin ( (75°+15°)/2) cos( (75°-15°)/2)\)?

Answer 12

I think this would help you.

Answer 13

I did (75°+15°)/2= 45

Answer 14

@3mar nice job - hope will can understanding the asker what is the key how is possible solving this easy exercise

Answer 15

I am using the sum-to-product formula

Answer 16

@TheSmartOne please sorry i not can reply to you just in this form again too

so i m here everyday to help and so in this way i ve arrived this 83"s level till today

Answer 17

but thank you for your question

Answer 18

\(5 \sin 75° + 5 \sin 15°\)

\(= 5 ( \sin 75° + \sin 15°)\)

for starters

then from:

\(\large \sin \theta \pm \sin \varphi =2\sin \left({\frac {\theta \pm \varphi }{2}}\right)\cos \left({\frac {\theta \mp \varphi }{2}}\right)\)

\(5 \left( \sin 75^o + \sin 15^o =2\sin \left({\frac {75^o + 15^o }{2}}\right)\cos \left({\frac {75^o - 15^o }{2}}\right) \right)\)

Answer 19

So I mean:
\[\large{ ~~~~5\sin(75)+5\sin(15)\\=5\sin(45+30)+5\sin(45-30)\\=5[\sin45\cos30+\cos30\sin45]+5[\sin45\cos30-\cos45\sin30]}\]

Can you continue from here?

Answer 20

yes @3mar tis was my idea too - the best easy way to solve it

Answer 21

5[sin45cos30+cos30sin45]+5[sin45cos30−cos45sin30]

5[2sin45 2cos30]+5[sin45cos30−cos45sin30] ? Is this right?

Answer 22

But I was told to solve it with Product to Sum formulas

http://www.sosmath.com/trig/prodform/prodform.html

Answer 23

thanky ou @3mar - sorry but i not can reply to you just in this way bc. my submitt buton is blocked again too

Answer 24

@IrishBoy123 That isn't the final answer is it?

Answer 25

So do you mean this?

Answer 26

I understand the last step from @IrishBoy123

And that is what I had in the beginning, but how to I simplify it for my final answer?

Answer 27

@3mar sorry but there where you wrote firstly the sin75 = sin(45+30) so please check it bc. there is one mistake

sin45cos30 +cos30sin45

so in this way is wrong

Answer 28

So I mean:
5sin(75)+5sin(15)=5sin(45+30)+5sin(45−30)=5[sin45cos30+cos30sin45]+5[sin45cos30−cos45sin30]


Can you continue from here?

Answer 29

do you see it now ?

Answer 30

@3mar No, I am using the Sum to Product Formulas

Answer 31

@jhonyy9
Thanks a lot.

I apology, my mistake!

\[\large{ ~~~~5\sin(75)+5\sin(15)\\=5\sin(45+30)+5\sin(45-30)\\=5[\sin45\cos30+\cos45\sin30]+5[\sin45\cos30-\cos45\sin30]}\]

But you are right, @Please.help.me

Answer 32

\(5 \left( 2\sin \left({\frac {75^o + 15^o }{2}}\right)\cos \left({\frac {75^o - 15^o }{2}}\right) \right)\)

\(= 10 \left( \sin {\frac {90^o }{2}} . \cos {\frac {60^o }{2}} \right)\)

\(= 10 \left( \frac {1 }{\sqrt 2} \frac{\sqrt{3}}{2} \right) = 5 \sqrt {\frac { 3 }{2}} \)

Answer 33

So you need to do like this:


You simplify!