Giải thích các bước giải:
Ta có:
$\tan\dfrac{a}{2}-\cot\dfrac{a}{2}=\dfrac{\sin\dfrac{a}{2}}{\cos\dfrac{a}{2}}-\dfrac{\cos\dfrac{a}{2}}{\sin\dfrac{a}{2}}$
$\to\tan\dfrac{a}{2}-\cot\dfrac{a}{2}=\dfrac{\sin^2\dfrac{a}{2}-\cos^2\dfrac{a}{2}}{\cos\dfrac{a}{2}\sin\dfrac{a}{2}}$
$\to\tan\dfrac{a}{2}-\cot\dfrac{a}{2}=-2\cdot\dfrac{\cos^2\dfrac{a}{2}-\sin^2\dfrac{a}{2}}{2\cos\dfrac{a}{2}\sin\dfrac{a}{2}}$
$\to\tan\dfrac{a}{2}-\cot\dfrac{a}{2}=-2\cdot\dfrac{\cos a}{\sin a}$
$\to\tan\dfrac{a}{2}-\cot\dfrac{a}{2}=-2\cot a$
$\to\tan\dfrac{a}{2}=\cot\dfrac{a}{2}-2\cot a$
