A community for students.
Here's the question you clicked on:
 0 viewing
shubham.bagrecha
 2 years ago
Prove that:
cos(A+B)+sin(AB)=2sin(45+A)cos(45+B)
shubham.bagrecha
 2 years ago
Prove that: cos(A+B)+sin(AB)=2sin(45+A)cos(45+B)

This Question is Closed

shubham.bagrecha
 2 years ago
Best ResponseYou've already chosen the best response.0\[ \cos(A+B)+\sin(AB)=2\sin(45+A)\cos(45+B)\]

Neo92
 2 years ago
Best ResponseYou've already chosen the best response.1first write cos(A+B) as sin[90(A+B)] then use sinC + sinD = 2sin[(C+D)/2]cos[(CD)/2] try and tell me what u get

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0ok ... for this first of all tell me what is cos(A+B)

shubham.bagrecha
 2 years ago
Best ResponseYou've already chosen the best response.0@Neo92 ok i will solve

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0cos(A+B)=sin(90AB) sin(90AB) + sin(AB) = 2sin(45+A)cos(45+B) we know that sin(x) + sin(y)=2sin([x+y]/2)cos([xy]/2)

mathslover
 2 years ago
Best ResponseYou've already chosen the best response.0so we get that sin(90AB) + sin(AB)=2sin(45B)cos(45A) but we know that sin(45B)=cos(90(45b))=cos(45+B) and cos(45A)=sin(90(45A))=sin(45+A) hence we get that cos(A+B) + sin(AB) = 2sin(45+A)cos(45+B)

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.2\[\cos(A+B)+\sin(AB)=\cos A\cos B\sin A\sin B+\sin A \cos B\sin B\cos A=\] \[=\cos A(\cos B\sin B)+\sin A (\cos B\sin B)=(\cos A+\sin A)(\cos B\sin B)\] Now use: \(\cos A+\sin A=\sqrt2\cdot(\frac1{\sqrt2}\cos A+\frac1{\sqrt2}\sin A)=\sqrt2\sin(45^\circ +A)\) and \(\cos B\sin B=\sqrt2\cdot(\frac1{\sqrt2}\cos B\frac1{\sqrt2}\sin B)=\sqrt2\cos(45^\circ +B)\). Now multiply this: \[(\cos A+\sin A)(\cos B\sin B)=\sqrt2\sin(45^\circ +A)\cdot \sqrt2\cos(45^\circ +B)=2\sin(45^\circ +A)\cdot\]\[\cdot\cos(45^\circ +B)\]
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.