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TRIGONOMETRY HELP: sec^2 X - 1 / sec^2 X?
Simplify and show work
sec^2 X - 1 / sec^2 X
5 Answers
- 8 years agoFavorite Answer
(sec(x)^2 - 1) / sec(x)^2 =>
tan(x)^2 / sec(x)^2 =>
(sin(x)^2 / cos(x)^2) / (1 / cos(x)^2) =>
sin(x)^2 / 1 =>
sin(x)^2
- 8 years ago
if its (sec^2 X -1)/ sec^2 X ..
Then this can be written as 1-(1/sec^2 X) due to the sec^2 X cancelling
Then 1/sec^2 X = cos^2 X hence it can be written as 1-cos^2 X
Now due too sin^2 X + cos^2 X = 1 then 1-cos^2 X = sin^2 X
so... (sec^2 X -1)/ sec^2 X = Sin^2 X
Source(s): A-level maths.. and going to do maths at uni - ?Lv 78 years ago
sec^2 x - 1 = tan^2 x
tan^2 x / sec^2 x = tan^2 x * cos^2 x = sin^2 x = 1 - cos^2 x = 1 - 1/sec^2 x
- Anonymous8 years ago
( sec^2 x - 1 ) / sec^2 x
= (sec^2 x / sec^2 x) - (1 / sec^2 x )
= 1 - cos^2 x
= sin^2 x + cos^2 x - cos^2 x
= Sin^2 x
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