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)

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

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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)

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

tan x = 1/ cot x or cot x * tan x = 1

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

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

**This proves that (tan A + cot B)(cot A - tan B) = cot A * cot B - tan A * tan B**