Asked by Shane
Prove the identity:
sec^4x - tan^4x = 1+2tan^2x
sec^4x - tan^4x = 1+2tan^2x
Answers
Answered by
DonHo
From left side:
sec^4x - tan^4x
factors into:
(sec(x)+tan(x))*(sec(x)-tan(x))*(sec^2(x) + tan^2(x))
(sec(x)+tan(x))*(sec(x)-tan(x)) =sec^2x - tan^2x
and from trig identity:
sec^2x - tan^2x = 1
left side:
1*(sec^2(x) + tan^2(x))
Right side:
1+2tan^2(x)
from the trig identity:
sec^2x - tan^2x = 1
sec^2x - tan^2x + 2tan^2x = 1+2tan^2x
simp lying this:
sec^2x + tan^2x
So right side now matches left side.
sec^4x - tan^4x
factors into:
(sec(x)+tan(x))*(sec(x)-tan(x))*(sec^2(x) + tan^2(x))
(sec(x)+tan(x))*(sec(x)-tan(x)) =sec^2x - tan^2x
and from trig identity:
sec^2x - tan^2x = 1
left side:
1*(sec^2(x) + tan^2(x))
Right side:
1+2tan^2(x)
from the trig identity:
sec^2x - tan^2x = 1
sec^2x - tan^2x + 2tan^2x = 1+2tan^2x
simp lying this:
sec^2x + tan^2x
So right side now matches left side.
Answered by
Anonymous
Steps r not clear
Answered by
Pp
Steps r not clear
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