Question

prove that (2+√3) ^2-4(2+√3) +1=0​

Answer 1

I don't now this answer is

Answer 2

Answer:

Answer

tan30=

3

1

1−tan

2

15

2tan15

=

3

1

Let tan15=a

2

3

a=1−a

2

a

2

+2

3

a−1=0

a=

2

−2

3

±

12+4

(∵tan15>0)

∴tan15=2−

3

1−tan

2

7

2

1

°

2tan7

2

1

°

=2−

3

Let tan7

2

1

°=b

2b=(2−

3

)(1−b

2

)

(2−

3

)b

2

+2b−(2−

3

)=0

∴b=

2(2−

3

)

−2+

4+4(2−

3

)

2

(∵tan7

2

1

°>0)

=

(2−

3

)

−1+

8−4

3

∴tan7

2

1

°=

2−

3

6

−

2

−1

tan82

2

1

°=cot7

2

1

°=

6

−

2

−1

2−

3

=

(

6

−(

2

+1))(

6

+

2

+1)

(2−

3

)(

6

+

2

+1)

=

6−(

2

+1)

2

2

6

−3

2

+2

2

−

6

+2−

3

=

3−2

2

6

−

2

+2−

3

=

(

2

−1)

2

(

2

−1)(

3

+

2

)

=

2

−1

3

+

2

=(

3

+

2

)(

2

+1)

∴tan82

2

1

°=(

3

+

2

)(

2

+1)