(sec 4 ø - sec 2 ø ) = tan 2 ø + tan 4ø
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Answer:
|| To prove: ||
sec^4 Ø - sec^2 Ø = tan^2 Ø + tan^4 Ø
|| Proof: ||
sec^4 Ø - sec^2 Ø = (sec^2 Ø)^2 - sec^2 Ø
=> (1 + tan^2 Ø)^2 - (1 + tan^2 Ø)
[We know that: sec^2 A = 1 + tan^2 A]
=> 1 + tan^4 Ø + 2tan^2 Ø - 1 - tan^2 Ø
=> tan^4 Ø + tan^2 Ø
proved.
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