b: cot a-tan a
=cosa/sina-sina/cosa
\(=\dfrac{cos^2a-sin^2a}{sina\cdot cosa}=cos2a:\dfrac{sin2a}{2}=2\cdot\dfrac{cos2a}{sin2a}=2\cdot cot2a\)
c: \(VT=tan\left(\dfrac{x}{2}\right)\cdot\left(\dfrac{1}{cosx}+1\right)\)
\(=tan\left(\dfrac{x}{2}\right)\cdot\dfrac{1+cosx}{sinx}\)
\(=\dfrac{sin\left(\dfrac{x}{2}\right)}{cos\left(\dfrac{x}{2}\right)}\cdot\dfrac{2\cdot cos^2\left(\dfrac{x}{2}\right)}{cosx}=\dfrac{2\cdot sin\left(\dfrac{x}{2}\right)\cdot cos\left(\dfrac{x}{2}\right)}{cosx}\)
=sinx/cosx=tanx
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