Skip to main content

how is tan (A+B) = [tan A + tan B]/[1 - tan A tan B]?

How is tan (A+B) = [tan A + tan B]/
[1 - tan A tan B]?

Method 1:
Let A = 30 deg and B = 45 deg.
LHS = tan (30+45) = tan 75 = 3.732050808
RHS = [tan A + tan B]/[1 - tan A tan B]
= [tan 30 + tan 45]/[1 - tan 30 tan 45]
= [0.577350269 + 1]/[1 - 0.577350269*1]
= 1.577350269/0.42264973
= 3.732050808 = LHS
Proved.
Method 2:
tan (A+B) = [tan A + tan B]/[1 - tan A tan B]
RHS = [tan A + tan B]/[1 - tan A tan B]
=[(sin A/cos A) + (sin B/cos B)]/[1-(sin A/cos A)(sin B/cos B)
= [sin A cos B + cos A sin B]/[cos A cos B][1 - sin A sin B/(cos A cos B)]
= sin (A+B)/{[cos A cos B][cos A cos B - sin A sin B]/(cos A cos B)}
= sin (A+B)/[cos A cos B - sin A sin B
= sin (A+B)/cos (A+B)
= tan (A+B) = LHS.
Proved.
Thanks.
source:Quara

Labels

Labels:

Comments

Post a Comment

Popular posts from this blog

area of sphere

Well ever wondered how the  Surface Area of a Sphere  was derived? Well here is a great visualisation to alter your perception. Step 1 : Cut the sphere in the following way. Step 2 : Spread the cut out part across the paper Step 3 : Collate the pieces together in the following way Step 4 : Spread the areas out separately to form a sine curve Step 5 : The area of the sine curve is the surface area of the sphere Here’s a  GIF file  for better understanding. There’s of course the generic method of calculation where the surface area is calculated by cutting the sphere into infinitesimally thin disks of varying radius stacked over one another and integrating them, but this above method is a different way to look at the same problem. Image Source: Google Images 220 Loves 284. Yes, this pair of numbers was considered as a symbol of love in medieval period, lovers used to send flowers, fruits to each other with these numbe...
Post a Comment
Read more

The Puzzle:

5 pirates of different ages have a treasure of 100 gold coins. On their ship, they decide to split the coins using this scheme: The oldest pirate proposes how to share the coins, and ALL pirates (including the oldest) vote for or against it. If 50% or more of the pirates vote for it, then the coins will be shared that way. Otherwise, the pirate proposing the scheme will be thrown overboard, and the process is repeated with the pirates that remain. As pirates tend to be a bloodthirsty bunch, if a pirate would get the same number of coins if he voted for or against a proposal, he will vote against so that the pirate who proposed the plan will be thrown overboard. Assuming that all 5 pirates are intelligent, rational, greedy, and do not wish to die, (and are rather good at math for pirates) what will happen?
Post a Comment
Read more