If cos 30=√3/2, prove that tan 15=2-√3
Answers
Answered by
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
)
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