Question

Find tan(450-a), If title=" \tan(a) = \frac{1}{2} " alt=" \tan(a) = \frac{1}{2} " align="absmiddle" class="latex-formula">
​

Answer 1

Answer:

$tan(450-a)=5\sqrt{3}-8$

Step-by-step explanation:

We know that:

$tan(a-b)=\frac{tan(a)-tan(b)}{1+tan(a)tan(b)}$

$tan(450-a)=\frac{tan(450)-tan(a)}{1+tan(450)tan(a)}$

Remember:

450°=360°+60°

and:

$tan(a)=\frac{1}{2}$

Thus:

$tan(450-a)=\frac{tan(60)-tan(a)}{1+tan(60)tan(a)}$

Then:

$tan(450-a)=5\sqrt{3}-8$