Given that tanx=p and sin2x=(2p)/(1+p^2). Without using table or calculator, find the value of tan15.
I let tan15=p, tan30=(2p)/(1-p^2)
p^2 + 2√3p-1=0
I still can't get the answer..
Follow Math Help Forum on Facebook and Google+
Originally Posted by Trefoil2727 Given that tanx=p and sin2x=(2p)/(1+p^2). Without using table or calculator, find the value of tan15. I assume that then .
Now if we have , so
And since that means , which means the solution is .
Tan x = p,
sin 2x = 2p/(1+p^2) let x = 15, Then we have
sin 30 = 2p /(1+p^2) = ½ that gives
Thus p = (4 ±√(16-12))/2 = (4 ±2√3)/2= 2 ±√3
Because 0 < 15 < 90 that is in first quadrant, we have
tan 15 = = 2- √3
View Tag Cloud