Question

√3(tan11+tan19) +tan11tan19​

Answer 1

Step-by-step explanation:

Given √3 (tan 11 + tan 19) + tan 11 tan 19

Given we need to find the value of √3 (tan 11 + tan 19) + tan 11 tan 19---------1

We know that tan (A + B) = tan A + tan B / 1 – tan A tan B

              So tan (11 + 19) = tan 11 + tan 19 / 1 – tan 11 tan 19

We know that tan (11 + 19) = tan 30 = 1 / √3

             So 1/√3 = tan 11 + tan 19 / 1 – tan 11 tan 19

          So √3 (tan 11 + tan 19) = 1 – tan 11 tan 19

Substituting this in 1 we get

            1 – tan 11 tan 19 + tan 11 tan 19

                            = 1

Answer 2

11+19=30

=>tan(11+19)°=tan30°

=>(tan11°+tan19°)/(1-tan11°tan19°)=1/√3

cross multiplication

=>√3(tan11°+tan19°)=1-tan11°tan19°

=>√3(tan11°+tan19°)+tan11°tan19°=1