MCQ
Choose the correct answer.
The value of $\tan75^\circ-\cot75^\circ$ is equal to: 
  • A
    $2\sqrt{3}$
  • B
    $2+\sqrt{3}$
  • C
    $2-\sqrt{3}$
  • D
    $1$

Answer

  1. $2\sqrt{3}$

Solution:

$\tan75^\circ-\cot75^\circ=\frac{\sin75^\circ}{\cos75^\circ}-\frac{\cos75^\circ}{\sin75^\circ}\\=\frac{2(\sin^275^\circ-\cos^275^\circ)}{2\sin75^\circ\cos75^\circ}=\frac{-2\cos150^\circ}{\sin150^\circ}$ 

$=-2\cot150^\circ=-2\cot(180^\circ-30^\circ)=2\cot30^\circ=2\sqrt3$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free