anonymous
  • anonymous
Trigonometry Proof How do you prove that ((cos(a+b))/(cosa +sinb))=((cosa - sinb)/(cos(b-a))) ?
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\[{\cos (a+b) \over {\cos a + \sin b}} = {{\cos a - \sin b} \over \cos (b-a)}\]
experimentX
  • experimentX
though no so sure .. !
phi
  • phi
cross multiply is good then use cos(a±b)= cos(a)cos(b)-/+ sin(a)sin(b) on the left

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
I have tried it forwards, backwards, cross multiplying to get 1, subtracting to get 0... I know I am missing some simple identity or transformation... but I have hit the wall.
experimentX
  • experimentX
cross multiply cos(a+b)cos(a-b) = (cos(a))^2-(sin(b))^2 1/2*(cos(2a)+cos(2b)) = 1/2 ( 2 cos^2a-1+1-2sin^2b) => rhs
anonymous
  • anonymous
I worked on this most of last night http://openstudy.com/updates/4f78bcb7e4b0ddcbb89e662b and it still bothers me; missing something simple somewhere
anonymous
  • anonymous
(cosa-sinb)(cosa+sinb) = cos^2 a -sin^2 b = (cos a)^2 -(1- cosb)^2 =cos ^2 a -1 +2cos ^b -cos^2 b cos(a+b) cos(b-a) = (cosa cosb-sina sinb)(cosb cos a +sinb sina) = (cos a cos b)^2 - (sin a sin b )^2 = (cos a cos b)^2 - ((1-cos^2 a) (1-cos ^2 b)) = (cos a cos b)^2 - (1-cos^2 a - cos ^2 b + cos^2 a cos^2 b) = -1 +cos^2 a + cos^2 b =(cosa-sinb)(cosa+sinb)
anonymous
  • anonymous
Thank you!

Looking for something else?

Not the answer you are looking for? Search for more explanations.