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Questions
Prove that:
`(tan A)/(1 + sec A) - (tan A)/(1 - sec A)` = 2 cosec A
Prove the following trigonometric identities:
`(tan A)/(1 + sec A) - (tan A)/(1 - sec A)` = 2 cosec A
Theorem
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Solution
LHS = `(tan A)/(1 + sec A) - (tan A)/(1 - sec A)`
= `tan A[1/(1 + sec A) - 1/(1 - sec A)]`
= `tan A[((1 - sec A) - (1 + sec A))/((1 + sec A) (1 - sec A))]`
= `tan A [(-2 sec A)/(1 - sec^2 A)]`
= `tan A [(-2 sec A)/(-tan^2 A)]`
= `(2 sec A)/(tan A)`
= `2 * 1/(cos A) * (cos A)/(sec A)`
= `2/(sin A)`
= 2 cosec A
= RHS
Hence proved.
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