Question

simplify by multiplying the conjugate (x-5)/((sqrtx+4)-3) and find exact values of
tan(7pi/6) please help with the summer work

Answer 1

\[if ~\it~is~\sqrt{x+4}-3 ?\]
\[\frac{ x-5 }{ \sqrt{x+4}-3 } \times \frac{ \sqrt{x+4}+3 }{ \sqrt{x+4}+3 }\]

Answer 2

\[=\frac{ \left( x-5 \right)\left( \sqrt{x+4}-3 \right) }{ x+4-9 }=?\]

Answer 3

it is +3 not -3

Answer 4

\[\tan \frac{ 7 \pi }{ 6 }=\tan \left( \pi+\frac{ \pi }{ 6 } \right)=\tan \frac{ \pi }{ 6 }=?\]

Answer 5

i got the first one but still little confuse on second one, can you please explain??

Answer 6

The tangent function is \(\pi\)-periodic. This means that \(\tan(x\pm\pi)=\tan x\), which allows you to do what @surjithayer suggested.