math
posted by michelle on .
How would you establish this identity:
(1+sec(beta))/(sec(beta))=(sin^2(beta))/(1cos(beta))
on the right, sin^2 = 1cos^2, that factor to 1cos * `1+cos, then the denominator makes the entire right side 1+cosB
which is 1+1/sec which is 1/sec (sec+1)
qed
using sec(beta) = 1/cos(beta):
1+sec(beta))/(sec(beta))= 1 + cos(beta)
sin^2(beta)/(1cos(beta)) =
(1cos^2(beta))/(1cos(beta)) =
1 + cos(beta)
This follows e.g. from:
(1  x^2) = (1  x)(1 + x)
and thus:
(1  x^2)/(1  x) = 1 + x

x=(1)