prove that tan 15° = 2-√3
Answers
Answered by
0
Answer:
RTP:
tan
15
=
2
−
√
3
tan
15
=
tan
(
45
−
30
)
Recall:
tan
(
a
−
b
)
=
tan
a
−
tan
b
1
+
tan
a
tan
b
tan
(
45
−
30
)
=
tan
45
−
tan
30
1
+
tan
45
tan
30
=
1
−
1
√
3
1
+
1
√
3
=
√
3
−
1
√
3
√
3
+
1
√
3
=
(
√
3
−
1
√
3
)
×
(
√
3
√
3
+
1
)
=
√
3
−
1
√
3
+
1
Rationalise the denominator
=
√
3
−
1
√
3
+
1
×
√
3
−
1
√
3
−
1
=
3
−
2
√
3
+
1
3
−
1
=
4
−
2
√
3
2
Take out the common factor
=
2
(
2
−
√
3
)
2
Simplify
=
2
−
√
3
Step-by-step explanation:
Answered by
0
Answer:
We know that,
tan(A.B)=
1+tanAtanB
tanA−tanB
tan(15)=tan(60−40)
1+
3
.1
3
−1
=
3
+1
3
−1
Rationalize:-
3
+1
3
−1
×
3
−1
3
−1
=
3−1
3+1−2
3
=2−
3
tan(15)=2−
3
Similar questions