SOLUTION: Given that tan A=1/5. Find the values of tan 2A, tan 4A and tan (45°-4A). I have calculated the value of tan 2A by using tan 2A = 2tan A/1-tan^2A and the answer I have got is 5/12

Algebra ->  Trigonometry-basics -> SOLUTION: Given that tan A=1/5. Find the values of tan 2A, tan 4A and tan (45°-4A). I have calculated the value of tan 2A by using tan 2A = 2tan A/1-tan^2A and the answer I have got is 5/12      Log On


   



Question 1117096: Given that tan A=1/5. Find the values of tan 2A, tan 4A and tan (45°-4A).
I have calculated the value of tan 2A by using tan 2A = 2tan A/1-tan^2A and the answer I have got is 5/12. Now I don't know how to solve further. Please give me a idea for it.

Answer by ikleyn(52831) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.  tan(2A) = %282%2Atan%28A%29%29%2F%281-tan%5E2%28A%29%29 = %282%2A%281%2F5%29%29%2F%281-%281%2F5%29%5E2%29 = %28%282%2F5%29%29%2F%281-1%2F25%29 = %28%282%2F5%29%29%2F%2824%2F25%29%29 = %282%2A25%29%2F%285%2A24%29 = 5%2F12.


    So, your calculations for tan(2A) are correct.




2.  To calculate  tan(4A),  notice that  4A = 2*(2A);  thus  tan(4A) = tan(2*(2A)).


    So, you can repeat THE SAME PROCEDURE  to get  tan(4A)  starting from  tan(2A), which you just know.




3.  tan(45°-4A) = %28tan%2845%5Eo%29-tan%284A%29%29%2F%281%2Btan%2845%5Eo%29%2Atan%284A%29%29 = %281-tan%284A%29%29%2F%281%2Btan%284A%29%29.


    So, when you will find  tan(4A)  (as I described in n.2), you will be in position to find  tan(45°-4A).