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If (secA+tanA)(secB+tanB)(secC+tanC)=(se...

If `(secA+tanA)(secB+tanB)(secC+tanC)=(secA-tanA)(secB-tanB)(secC-tanC),` prove that the value of each side is +-1.

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Let
`(secA+tanA)(secB+tanB)(secC+tanC)=x (i)`
`:. (secA-tanA)(secB-tanB)(secC-tanC)=x (ii)`
Multiplying Eqs.(i) and (ii), we get
`(sec^2A-tan^2A)(sec^2B-tan^2B)(sex^2C-tan^2C)=x^2`
or `x^2=1`
`:. x=pm1`
Hence, each side is equal to `pm1`.
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