Question

PLS HELP FAST! :

tan(A - B) = tanA - tanB / 1+tanATanB (given)

Evaluate tan 15 degree

Answer 1

tan(45-30)= tan45-tan30/1+tan45.tan30

tan15= (1-1/√3)/(1+1/√3) = (√3-1)/(√3+1)

or. Rationalising

= (√3-1)^2/2
= (4-2√3)/2
= 2-√3

Answer 2

Tan 15

Tan(45 - 30)

Tan(A - B) = Tan A - Tan B/1 + Tan A Tan B

$\frac{Tan 45 - Tan 30}{1 + Tan 45 Tan 30}$

$\frac{1 - \frac{1}{ \sqrt{3} } }{1 + \frac{1}{ \sqrt{3} } }$

$\frac{ \sqrt{3}-1 }{ \sqrt{3}+ 1 }$

$\frac{( \sqrt{3} - 1)^2 }{ \sqrt{3}^2 - 1^2 }$

$\frac{3 + 1 - 2 \sqrt{3} }{2}$

On rationalizing, we get

$\frac{4 - 2 \sqrt{3} }{2}$

$\frac{2(2 - \sqrt{3} )}{2}$

$2 - \sqrt{3}$


Hope this helps!