Prove that sec^2a - sin^2a-2sin^4a/2cos^4a-cos^2a=1
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=Sec²a - (sin²a [1-2sin²a])/(cos²a[2cos²a -1])
= sec²a - tan²a [1- 2sin²a]/[2cos²a -1]
= sec²a - tan²a [1- sin²a - sin²a]/ [cos²a + cos²a -1]
= sec²a - tan²a [ cos ²a - sin ²a]/[cos2a
- sin²a]
= sec²a - tan²a *1 .
= sec²a - tan²a
= 1
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