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Question
Prove the following:
`1/(1 - cosA) - 1/(1 + cosA)` = 2cot A cosec A
Theorem
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Solution
LHS = `((1 + cosA) - (1 - cosA))/((1 - cos A)(1 + cos A))`
`((1 + cosA - 1 + cosA))/((1 - cos A)(1 + cos A)) = (2 cosA)/((1 - cosA)(1 + cosA))`
⇒ `(2cosA)/(1 - cos^2A)`
⇒ `(2cosA)/(sin^2A)`
⇒ `2.cosA/sinA. 1/sinA`
Since `cosA/sinA = cotA and 1/sinA = "cosec"A`
LHS = RHS
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