Question

sin(5pi/12)+sin(pi/12)
what is the exact value using sum to product identities?
Please help!

Answer 1

hi,
\[\sin C + \sin D = 2\sin( \frac{ C +D }{ 2 })\cos(\frac{ C-D }{ 2 })\]

so... we can write ur answer...
\[\sin \frac{ 5 \pi }{ 12} + \sin \frac{ \pi }{12 } = 2\sin(\frac{ 5 \pi + \pi }{ 12 \times 2 })\cos( \frac{ 5 \pi - \pi }{12 \times 2 })\]\[2 \sin \frac{ 6 \pi }{24 }\cos \frac{ 4 \pi }{ 24 }\]\[2 \sin \frac{ \pi }{ 4 }\cos \frac{ \pi }{6 }\]

now...
\[\sin \frac{ \pi }{ 4 } = \frac{ 1 }{ \sqrt{2} } \ and \ \cos \frac{ \pi }{ 6 } =\frac{ \sqrt{3} }{ 2 }\]

which means...\[\sin \frac{ 5 \pi }{12 } + \cos \frac{ \pi }{12 } = 2 \times \frac{ 1 }{\sqrt{2} } \times \frac{ \sqrt{3} }{ 2 }\]
\[= \frac{ \sqrt{3} }{ \sqrt{2}} = \frac{ \sqrt{6} }{ 2}\]

Hope this will help ya!!

Answer 2

yes thank you ! i didnt add the 12+12 at the bottom so keep getting wrong/

Answer 3

hah.. but now u got it correct!! that's the important part!!