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 Trig trick (Posted on 2002-11-07)
Prove that
sinē x + cosē x = 1

 See The Solution Submitted by Dulanjana Rating: 2.1818 (11 votes)

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 Solution | Comment 12 of 13 |

Let us consider a right angled triangle ABC with AB, BC and AC
respectively as the altitude, base and the hypotenuse, where
< ABC = 90 degrees.

Then, AB^2 + BC^2 = AC^2
Or, (AB/AC)^2 + (BC/AC)^2 = 1........(*)

We know that:

sin x = altitude/ hypotenuse = AB/ AC
cos x = base/ hypotenuse = BC/AC

Thus, from (*) we obtain:

sin^2(x) + cos^2(x) = 1

 Posted by K Sengupta on 2007-05-28 12:06:41
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