Question

if tan15=2-√3,then find the value of tan75

Answer 1

hi friend,

given tan15=2-√3

=tan(90-75)=2-√3

=cot 75 =2-√3

=1/tan75=2-√3

tan75=1/2-√3

multiplying and dividing with 2+√3,we get

tan75=2+√3/(4-3)

tan75=2+√3

I hope this will help u :)

Answer 2

Answer:

$Tan 75=2+\sqrt{3}$

Step-by-step explanation:

Given :$Tan 15 = 2-\sqrt{3}$

To Find : Value of tan 75

Solution :

$Tan (90-75) = 2-\sqrt{3}$

Identity : $Tan(90-\theta)=cot \theta$

$Cot 75 = 2-\sqrt{3}$

Identity : $cot \theta = \frac{1}{tan \theta}$

$\frac{1}{tan 75} = 2-\sqrt{3}$

$\frac{1}{2-\sqrt{3}} = tan 75$

$\frac{1}{2-\sqrt{3}} \times \frac{2+\sqrt{3}}{2+\sqrt{3}} = tan 75$

Identity : $(a+b)(a-b)=a^2-b^2$

$\frac{2+\sqrt{3}}{4-3} = tan 75$

$2+\sqrt{3}= tan 75$

Hence $Tan 75=2+\sqrt{3}$