Prove the following identities: 1+(secA-tanA)2cosecA(secA-tanA)=2tanA - Mathematics

Prove the following identities:

`(1 + (secA - tanA)^2)/(cosecA(secA - tanA)) = 2tanA`

Sum

`(1 + (secA - tanA)^2)/(cosecA(secA - tanA))`

= `((sec^2A - tan^2A) + (secA - tanA)^2)/(cosecA(secA - tanA))`

= `((secA - tanA)(secA + tanA) + (secA + tanA)^2)/(cosecA(secA - tanA))`

= `((secA + tanA) + (secA - tanA))/(cosecA)`

= `(2secA)/(cosecA)`

= `2(1/cosA)/(1/sinA)`

= 2 tanA

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