Question

Tan75 degree+cot75degree=?

Answer 1

Answer:

The answer is 4

Step-by-step explanation:

  $\tan75^\circ+\cot75^\circ$

$=\dfrac{\sin75^\circ}{\cos75^\circ}+\dfrac{\cos 75^\circ}{\sin 75^\circ}\\\\=\dfrac{\sin^275^\circ+\cos^275^\circ}{\cos 75^\circ\sin 75^\circ}\\\\=\dfrac{2}{2\cos 75^\circ\sin 75^\circ}=\dfrac{2}{\sin 2(75^\circ)}=\dfrac{2}{\sin 150^\circ}$   $\boxed{\because \sin 2\theta=2\sin\theta\cos\theta}$

 $=\dfrac{2}{\sin(180^\circ-30^\circ)}=\dfrac{2}{\sin 30^\circ}=\dfrac{2}{\frac{1}{2}}=4$