Without using calculator or table of multiplication, show that $tan 195° = (sqrt3-1)/(sqrt3+1)$ .?

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Answer 1 · 2018-04-11T02:24:36

$LHS=tan195^@$

$=tan(180^@+15^@)$

$=tan(15^@)$

$=tan(60^@-45^@)$

$=(tan60^@-tan45^@)/(1+tan60^@tan45^@)$

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

$=(sqrt3-1)/(sqrt3+1)=RHS$

Without using calculator or table of multiplication, show that tan 195° = (sqrt3-1)/(sqrt3+1)tan 195° = (sqrt3-1)/(sqrt3+1).?