Simplify? Tan 135- Tan 15 divided by 1+ Tan 135 Tan15

1 Answer
maganbhai P.
Mar 22, 2018

#-sqrt3#

Explanation:

We know that

#(1)tan(180-theta)=tan(pi-theta)=-tantheta,... to2^(nd) #quadrant

#color(red)((2)tan(A-B)=(tanA-tanB)/(1+tanAtanB)#

We use above#color(red)((2)# from #RHS toLHS#,

where #A=135^0 andB=15^0#

#(tan135-tan15)/(1+tan135tan15)=tan(135-15)#

#(tan135-tan15)/(1+tan135tan15)=tan120#

#(tan135-tan15)/(1+tan135tan15)=tan(180-60),..to#Apply (1)

#(tan135-tan15)/(1+tan135tan15)=-tan60=-sqrt3#

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