Tuesday, August 19, 2014

prove the following: (tan A + cot B) (cot A - tan B) = cot A cot B - tan A tan B

We have to prove that: (tan A + cot B) (cot A - tan B) =
cot A cot B - tan A tan B


(tan A + cot B) (cot A - tan
B)


open the brackets and multiply the
terms.


=> tan A * cot A - tan A * tan B + cot A *
cot B - cot B * tan B


Use the relation tan x * cot x =
1


=> 1 - tan A * tan B + cot A * cot B -
1


=> - tan A * tan B + cot A * cot
B


=> cot A * cot B - tan A * tan
B


This proves the identity (tan A + cot B)
(cot A - tan B) = cot A cot B - tan A tan B

No comments:

Post a Comment

Can (sec x - cosec x) / (tan x - cot x) be simplified further?

Given the expression ( sec x - csec x ) / (tan x - cot x) We need to simplify. We will use trigonometric identities ...