Question

Find the values of -

`[tan 60°]/[sin 60° + cos 60°]`

Answer 1

` [tan 60°]/ [ sin 60° + cos 60°]`

= `sqrt 3/{sqrt3/2 + 1/2}`

= `sqrt 3/[(sqrt 3  +  1)/2]`

= `sqrt3 xx 2/(sqrt3 + 1)`

= `(2 sqrt3)/(sqrt3 + 1)`

= `(2sqrt3(sqrt3-1))/((sqrt3+1)(sqrt3+1)`   

= `(2sqrt3(sqrt3-1))/((sqrt3)^2 - (1)^2)`     ...[∵ (a + b) (a - b) = a² - b²]

= `(2sqrt3(sqrt3-1))/(3-1)`

= `(2sqrt3(sqrt3-1))/(2)`

= `sqrt3(sqrt3-1)`