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

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Answer 1 · 2016-08-15T18:41:39

$-(2+sqrt3)$ .

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

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

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

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

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

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

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

$=-(2+sqrt3)$ .

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