Today I have a very simple question from Yahoo Answers. Hopefully tomorrow I'll be able to find something a little more interesting:
Prove that tan2 x + 1 = sec2 x
Every trigonometry student must remember this identity, but here is the reason why the trig students must know this identity:
As you all should know, sin2 x + cos2 x = 1 (if you don't know that, blame your math teacher). Now all we have to do is use some more trigonometric identities and rules of exponents, and we're all set:
tan x = sin x/cos x
sec x = 1/cos x
(a/b)n = an/bn
Now we take the basic trigonometric identity and divide it by cos2 x:
sin2 x / cos2 x + cos2 x / cos2 x = 1 / cos2 x
(sin x / cos x)2 + 1 = (1/cos x)2
tan2 x + 1 = sec2 x
Simple, nice, and easy.
Bring in more questions!
Nadav
nadavs
Monday, May 19, 2008
Trigonometry on the Table
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1 comment:
This is a nice pleasant math site. The layout is smoothing. Maybe because I like blue colour.
The explanation of the identities are clear too.
I am happy to see a site close to mine.
It is the sharing of math knowledge to our viewers that make me feel good blogging about math.
Through this way, we are able to help any math learners reduce the obstacles they face studying math.
Maths is interesting!
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