How do you simplify using the sum and difference formula #tan(285)#?

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Answer 1 · 2016-08-15T18:41:39

#-(2+sqrt3)#.

#tan285^@=tan(360^@-75^@)=-tan75^@=-tan(45^@+30^@)#

#=-{(tan45^@+tan30^@)/(1-tan45^@*tan30^@)}#

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

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

#=-{(sqrt3+1)/(sqrt3-1)*(sqrt3+1)/(sqrt3+1)}#

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

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

#=-(2+sqrt3)#.