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Question
Prove the following:
`1/(tan3"A" - tan"A") - 1/(cot3"A" - cot"A")` = cot2A
Solution
L.H.S. = `1/(tan3"A" - tan"A") - 1/(cot3"A" - cot"A")`
= `1/(tan3"A" - tan"A") - 1/(1/(tan3"A") - 1/tan"A"`
= `1/(tan3"A" - tan"A") - (tan3"A"*tan"A")/(tan"A" - tan3"A")`
= `1/(tan3"A" - tan"A") + (tan3"A"*tan"A")/(tan3"A" - tan"A")`
= `(1 + tan3"A"*tan"A")/(tan3"A" - tan"A")`
= `1/(((tan3"A" - tan"A")/(1 + tan3"A"*tan"A"))`
= `1/(tan(3"A" - "A"))`
= `1/(tan2"A")`
= cot 2A
= R.H.S.
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