Find the exact value of tan 22.5 by using the expression for tan2x.
Medal will be given for best ans

Question

anonymous · Answer

11.25

anonymous · Answer

The textbook answer is apparently: $$\sqrt{2} -1$$

sidsiddhartha · Answer

use tan2a=2tana/(1-tan^2a)
so 
tan45=2tan22.5/(1-tan^22.5)

tan45=1 so 
tan^22.5+2*tan22.5-1=0
solve it

sidsiddhartha · Answer

sorry made a mistake 
tan45=2tan22.5/[1-tan^2(22.5)]

anonymous · Answer

tan 45 = 2tan22.5 / 1-tan^2 22.5 
1 = 2tan22.5 / 1- tan^2 22.5 
by cross multiplication u get: 
1- tan^2 22.5 = 2tan 22.5 
u get a quadratic and solving it you'll get 2 ans : -1+sqrt2 and -1-sqrt2 
but only fist one is right cause 22.5 is in 1st quadrant and hence tan22.5 should be positive.So the second one will be wrong ans

sidsiddhartha · Answer

so it will look like|dw:1399368076386:dw|
so ur ans is =sqrt(2)-1