Question

If cos 30=√3/2, prove that tan 15=2-√3

Answer 1

Step-by-step explanation:

Half angle formulae for

tan

(

θ

)

2

XXX

=

sin

(

θ

)

1

+

cos

(

θ

)

xxxxxxxx

[1]

XXX

=

cos

(

θ

)

1

−

sin

(

θ

)

xxxxxxxx

[2]

XXX

=

±

√

1

−

cos

(

θ

)

1

+

cos

(

θ

)

xxxx

[3]

Since

sin

(

30

∘

)

=

1

2

xx

and

xx

cos

(

30

∘

)

=

√

3

2

We can use [2] (for example) to get

tan

(

15

∘

)

=

tan

(

30

∘

2

)

=

(

√

3

2

)

(

1

−

1

2

)