## ¿Did_You_Know? 3 years ago Evaluate: tan105deg using the sum and difference formulas. I

1. akash_809

tan(a+b)=(tan a +tan b)/(1-tan a tan b)....put a =60 and b =45 and solve

2. ¿Did_You_Know?

where u got 60 and 45?

3. akash_809

tan(60+45)=tan105...right

4. akash_809

can u do it nw

5. akash_809

tan 60 =$\sqrt{3}$ and tan 45 =1

6. ¿Did_You_Know?

i am getting stuck at the part where it is: |dw:1347964171044:dw|

7. akash_809

so $\tan105= (1+\sqrt{3})/(1-\sqrt{3})$

8. akash_809

|dw:1347964267571:dw|

9. akash_809

can u solve this now

10. ¿Did_You_Know?

wait. why did you square that?

11. akash_809

|dw:1347965085424:dw|

12. ¿Did_You_Know?

arent you suppposed to mutliply it by the bottom one?

13. akash_809

no it is rationalization u multiply num and den both by a coomon value so that the expression remains unaffected

14. ¿Did_You_Know?

so it is always the numerator?

15. akash_809

no depends on what simplifies the root if 1-root 3 was there in numerator and 1+root 3 in den the you would multiply num and den by 1-root 3...since (1+root 3)(1-root3)=1-3...using a^2-b^2

16. ¿Did_You_Know?

how would you know which one to multiply by tho?

17. akash_809

multiply with a value that would make denominator a rational one