How do you find the exact value for $(5tan60°) / cos30°$ ?

Question

2835 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-08T06:04:32

You can do this without a calculator and with few manipulations.

$(5tan60^o)/(cos30^o) = (5sin60^o)/[(cos30^o)(cos60^o)]$

but

$sin(pi/2 - x) = cosx$

Therefore:

$sin(90^o - overbrace(30^o)^x) = sin60^o = cos30^o$

$=> (5cancel(sin60^o))/[cancel((cos30^o))(cos60^o)]$

$= (5cancel(sqrt3/2))/(cancel(sqrt3/2)*1/2)$

$= 10$

How do you find the exact value for (5tan60°) / cos30°(5tan60°) / cos30°?