Question

find the exact value of tan (-15) using the sum/difference identities

Answer 1

Form trigonometric ratios,

,

We know the trigonometric fromulas that ,

  

Here, we have to find the value of tan(-15), so to use the above formula we can write (-15) as (30-45)

Now,

So,

  

   

  

Now , rationalize the denominator, first taking negative common from numerator.

  

Since, from algebra,  (a+b)(a-b) = a^2-b^2 ​​​​​​

and (a-b)^2 = a^2 + b^2 - 2*a*b

  

  

So,.   tan(-15) = -(2-√3)