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Prove that: sec^4A(1-sin^4A) -2 tan^2A...

Prove that:
`sec^4A(1-sin^4A) -2 tan^2A=1`.

Text Solution

Verified by Experts

`sec^4A(1-sin^4A) -2 tan^2A `
=`(1)/(cos^4A) xx(1-sin^2A)(1+sin^2A)-2 sin^2A/cos^2A`
`(1)/(cos^4A) xx(cos^2A)(1+sin^2A)-2 sin^2A/cos^2A`
`[(therefore sin^2A + cos^2A = 1)/(therefore 1-sin^2A = cos^2A)]`
`(1+sin^2A)/(cos^2A)-(2sin^2A)/(cos^2A)`
`(1+sin^2A-2sin^2A)/(cos^2A)`
`(1-sin^2A)/(cos^2A)=(cos^2A)/(cos^2A)=1`
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