Question

evaluate tan15° tan25° tan60° tan65° tan75°- tan30°​

Answer 1

Answer:

$\frac{2}{\sqrt{3} }$

Step-by-step explanation:

{ tan15° tan25° tan60° tan65° tan75°}- tan30°​

=> { tan15° tan25° tan60° tan(90 - 25)° tan(90 - 15)° } - tan 30°

• Since, tan(90 - Ф) = cotФ

=> {tan15° tan 25° tan60° cot25° cot15°} - tan 30°

• cot Ф = 1/ TanФ

=> {tan15° tan25° tan60° (1/ tan15°) (1/ tan 25°)} - tan 30°

=> {tan60°} - tan 30°

We know that,

• tan 60 = √3

• tan 30 = 1/ √3

=> √3 - 1/ √3

=> (3 - 1)/ √3

=> 2/ √3

                             

Hope this helps!