Question

If tan $tan22{\frac{1}{2}}^{\circ }=x$ what is the value of tan${135}^{\circ }$?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

tan135 = tan (90+45)

= -cot 45

= - $\frac{1}{tan45}$

We expressed it in terms of tan45 because we can easily calculate tan45 since tan 22 $\frac{1}{2}$ is given .

Tan 45 = tan 2 × 22 $\frac{1}{2}$

= $\frac{2tan22\frac{1}{2}}{1-ta{n}^{2}22\frac{1}{2}}$

= $\frac{2x}{1-x^2}$

$\Rightarrow$ tan 135 = $\frac{-1}{\frac{2x}{1-x^2}}$

= $\frac{x^2-1}{2x}$

key steps / concepts : (1) Expressing tan 135^\circ in terms of tan45^\circ