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How would you establish this identity:

(1+sec(beta))/(sec(beta))=(sin^2(beta))/(1-cos(beta))

on the right, sin^2 = 1-cos^2, that factor to 1-cos * `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)/(1-cos(beta)) =

(1-cos^2(beta))/(1-cos(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

  • math -

    x=(-1)

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