Question

If $\tan {30}^0=x,\tan {45}^0=y,\tan {60}^0=z,$ then which of the following is/are correct?

• A. $x+y=z$
• B. $xy=z$
• C. $xz=y$
• D. $y+z=x$

Answer 1

The correct option is C $xz=y$

$x=\tan {30}^{\circ }=\frac{1}{\sqrt{3}},y=\tan {45}^{\circ }=1,z=\tan {60}^{\circ }=\sqrt{3}$

$xz=\frac{\sqrt{3}}{\sqrt{3}}=1=y$

$x+y=\frac{1}{\sqrt{3}}+1=\frac{1+\sqrt{3}}{\sqrt{3}}\ne \sqrt{3}=z$

$y+z=1+\sqrt{3}\ne \frac{1}{\sqrt{3}}=x$