A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
i need to prove sin(u+v)sin(uv)=sin^2usin^2v
anonymous
 5 years ago
i need to prove sin(u+v)sin(uv)=sin^2usin^2v

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Let's use trigonometric identity: \[\sin(u \pm v) = \sin(u)\cos(v) \pm \cos(u)\sin(v)\] Rewrite original expression to \[(sin(u)cos(v) + cos(u)sin(v))(sin(u)cos(v)  cos(u)sin(v))\] Now, the key thing is that it is a product of sum and difference which is known from \[(a+b)(ab) = a^2  b^2\] So, the expression above will be just \[(\sin(u)\cos(v))^2  (\cos(u)\sin(v))^2\] Now, we can rewrite this as \[{1 \over 4}[(1\cos(2u))(1 + \cos(2v))  (1\cos(2v))(1+\cos(2u))]\] Then, rewrite this as \[{1 \over 4}[(1  \cos^2 u + \sin^2u)(1+\cos^2v  \sin^2v)  (1\cos^2v+\sin^2v)(1+\cos^2u  \sin^2u)]\] (as you can see, there is pretty much of work to do with this). Now, we rewrite as: \[{1 \over 4}[(2\sin^2u)(2  2\sin^2v)  (2\sin^2v)(2  2\sin^2u)]\] This in turn can be rewrited as \[{1 \over 4}[(4\sin^2u  4(\sin^2(u)\sin^2(v)))  (4\sin^2v  4(\sin^2(u)\sin^2(v)))]\] which equals to \[{1 \over 4}(4 \sin^2u  4 \sin^2v)\] which finally is \[sin^2u  sin^2v\]
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.