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factor formulae c3

factor formulae:

cosA+cosB = 2 cos (A+B/2) cos (A-B / 2)

can someone pls explain how to go from the RHS to the LHS (not the usual way).. i am stuck at this eg. 2 cos (A+40) cos (A-10) = 1 and i dont know how to take it back to the original ( the angles)
Original post by pondsteps
factor formulae:

cosA+cosB = 2 cos (A+B/2) cos (A-B / 2)

can someone pls explain how to go from the RHS to the LHS (not the usual way).. i am stuck at this eg. 2 cos (A+40) cos (A-10) = 1 and i dont know how to take it back to the original ( the angles)


2cos⁡(2A+802)cos⁡(2A−202)\displaystyle 2\cos(\frac{2A+80}{2})\cos(\frac{2A-20}{2})

=2cos⁡((2A+30)+502)cos⁡((2A+30)−502)=...\displaystyle =2\cos(\frac{(2A+30)+50}{2})\cos(\frac{(2A+30)-50}{2})=...

and get it into the form on the LHS, if that's what you're trying to do.
Original post by RDKGames
2cos⁡(2A+802)cos⁡(2A−202)\displaystyle 2\cos(\frac{2A+80}{2})\cos(\frac{2A-20}{2})

=2cos⁡((2A+30)+502)cos⁡((2A+30)−502)=...\displaystyle =2\cos(\frac{(2A+30)+50}{2})\cos(\frac{(2A+30)-50}{2})=...

and get it into the form on the LHS, if that's what you're trying to do.


can u please explain the second step!!
Original post by pondsteps
can u please explain the second step!!


Find the difference between 80 and -20 and divide it by 2. You need a midpoint between the two which is 30, then you just add/subtract the 50 on either side to make it fit the form of the identity as you add/subtract B there.
Original post by RDKGames
Find the difference between 80 and -20 and divide it by 2. You need a midpoint between the two which is 30, then you just add/subtract the 50 on either side to make it fit the form of the identity as you add/subtract B there.


do u have any clue if this is required in the c34 (c3 /c4) modules???? it was never explained to us and i cant seem to get it!
Original post by pondsteps
do u have any clue if this is required in the c34 (c3 /c4) modules???? it was never explained to us and i cant seem to get it!


No idea, I've never used these formulae for my A-Level maths. Ask your teacher.
its not mentioned in the syllabus but its written in the exam data booklet ughhh ..
Original post by RDKGames
No idea, I've never used these formulae for my A-Level maths. Ask your teacher.


2.PNG
is this the same as ur way ??
Original post by pondsteps

is this the same as ur way ??


I think they made the second step slightly more confusing than my approach, but ultimately the third line is what you end up with if you apply the identity to my approach and carry on from that step onwards.

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