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Question
Prove the following trigonometric identities.
`(1 + cos A)/sin^2 A = 1/(1 - cos A)`
Solution
We need to prove `(1 + cos A)/sin^2 A = 1/(1 - cos A)`
Using the property `cos^2 theta + sin^2 theta = 1` we get
LHS = `(1 + cos A)/sin^2 A = (1 + cos A)/(1 - cos^2 A)`
Further using the identity, `a^2 - b^2 = (a + b)(a - b)` we get
`(1 + cos A)/(1 - cos A) = (1 + cos A)/((1 - cos A)(1 + cos A))`
`= 1/(1 - cos A)`
= RHS
Hence proved.
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