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
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