How do you prove $(1+sinx)/(1-sinx)+(sinx-1)/(1+sinx)$ ?

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Answer 1 · 2016-10-23T02:01:56

The expression simplifies to $4sinxsec^2x$ .

Put on a common denominator.

$=((1 + sinx)(1 + sinx))/((1 -sinx)(1 + sinx)) + ((sinx - 1)(1 - sinx))/((1 + sinx)(1 - sinx))$

$=(1 + 2sinx + sin^2x - sin^2x + sinx + sinx - 1)/(1 - sin^2x)$

Apply the identity $sin^2theta + cos^2theta = 1 -> cos^2theta = 1 - sin^2theta$ to the numerator and simply the denominator.

$=(4sinx)/cos^2x$

Apply the identity $1/cosbeta = secbeta$ .

$=4sinxsec^2x$

Hopefully this helps!

How do you prove (1+sinx)/(1-sinx)+(sinx-1)/(1+sinx)(1+sinx)/(1-sinx)+(sinx-1)/(1+sinx)?