Question

If (tanA + tan30)/(1-tanAtan30)=-1 Determine the value of tanA?

Answer 1

`tanA=-(2+sqrt3)`

Explanation:

`"using the "color(blue)"exact value of the trig. ratio"`

`•color(white)(x)tan30^@=1/sqrt3`

`(tanA+tan30)/(1-tanAtan30)=-1larrcolor(blue)"cross multiply"`

`rArrtanA+tan30=-1+tanAtan30`

`rArrtanA-tanAtan30=-1-tan30`

`rArrtanA(1-tan30)=-1-tan30`

`rArrtanA=(-1-tan30)/(1-tan30)`

`color(white)(rArrtanA)=(-1-1/sqrt3)/(1-1/sqrt3)xxsqrt3/sqrt3`

`"multiply numerator/denominator by the "color(blue)"conjugate"`
`"of the denominator"`

`color(white)(rArrtanA)=(-sqrt3-1)/(sqrt3-1)xx(sqrt3+1)/(sqrt3+1)`

`color(white)(rArrtanA)=(-4-2sqrt3)/2`

`color(white)(rArrtanA)=-2-sqrt3=-(2+sqrt3)`