How do you use the angle sum or difference identity to find the exact value of #tan195#?

Question

15709 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-04T08:48:51

#tan195^o=2-sqrt3#

We use #tan150^o=tan(180^o-30^o)=-1/sqrt3# and #tan45^o=1#

Therefore #tan195^o=tan(150^o +45^o)#

= #(-1/sqrt3+1)/(1-(-1/sqrt3)xx1)#

= #(1-1/sqrt3)/(1+1/sqrt3)#

Now multiplying numerator and denominator by #sqrt3#

#tan195^o=(sqrt3-1)/(sqrt3+1)#

= #(sqrt3-1)^2/((sqrt3+1)(sqrt3-1))#

= #3+1-2sqrt3)/(3-1)#

= #(4-2sqrt3)/2#

= #2-sqrt3#