Question

tan(x/2) cos^2(x) - tan(x/2) = [sin(x)/sec(x)] - sin(x)
provide that this equation equals the other using identities.

Answer 1

\[= \sqrt{1-cosx}/\sqrt{1+cosx} * (\cos^{2}x - 1)\]
\[= \sqrt{1-cosx}/\sqrt{1+cosx} * (\cos^{2}x - 1) * \sqrt{1+cosx}/\sqrt{1+cosx}\]
\[= \sqrt{1-cos^{2}x}* (cosx- 1) * (cosx+ 1)/ \sqrt{(1+cosx)^{2}}\]
\[= \sqrt{sin^{2}x}* (cosx- 1) \]
\[= sinx* (cosx- 1) \]

Answer 2

Oops. Abs of sinx