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The simplified value of `(secA-cosA)^(2)+(co s e c A-sinA)^(2)-(cotA-tanA)^(2)`.

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Correct Answer - c
`(secA-cosA)^(2)+(co s ecA-sinA)^(2)-(cotA-tanA)^(2)`
`=(sec^(2)A+cos^(2)A-2secAcosA)`
`+(co s ec^(2)A+sin^(2)A=2co s ecAsinA)`
`-(cot^(2)A+tan^(2)A-2cotAtanA)`
`=sec^(2)A-tan^(2)A+cos^(2)+sin^(2)A`
`+co s ec^(2)A-cot^(2)A-2`
`=3-2=1`
Alternate shortcut method
`(secA-cosA)^(2)+(co s ecA-sinA)^(2)-(cotA-tanA)^(2)`
put `theta=45^(@)`
`=(sec45^(@)-cos45^(@))^(2)+(co s ec45^(@)-sin45^(@))^(2)-(cot45^(@)-tan45^(@))^(2)`
`=(sqrt(2)-(1)/sqrt(2))^(2)+(sqrt(2)-(1)/sqrt(2))^(2)-(1-1)^(2)`
`=(1)/(2)+(1)/(2)-0=1`

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