1- tan²1/2 /
2 tan 71/2
Answers
Step-by-step explanation:
MATHS
Prove that: cot7
2
1
∘
=
2
+
3
+
4
+
6
ANSWER
cot7
2
1
°
=
2
+
3
+
4
+
6
⇒L.H.S=cot7
2
1
°
=cot
2
15
°
=
sin(
2
15
)
°
cos(
2
15
)
°
=
2sin(
2
15
)
°
2cos(
2
15
)
°
=
2sin(
2
15
)
°
cos(
2
15
)
°
2cos
2
(
2
15
)
°
=
sin15°
1+cos15°
[∵1+cos2θ=2cos
2
2
2θ
]
[&2sin
2
θ
.cos
2
θ
=sin
2
2θ
]
⇒cos15°=
4
1
(
6
+
2
)&sin15°=
4
1
(
6
−
2
)
∴LHS=
4
1
(
6
−
2
)
1+
4
1
(
6
+
2
)
=
6
−
2
4+
6
+
2
Apply componendo and dividendo, we get
⇒LHS=
(
6
−
2
)(
6
+
2
)
(4+
6
+
2
)(
6
+
2
)
=
6−2
4
6
+4
2
+6+
12
+
12
+2
=
4
4
6
+4
2
+8+2
3
+2
3
=
4
8
+
4
4
2
+
4
4
3
+
4
4
6
=2+
2
+
3
+
6
=
2
+
3
+
4
+
6
⇒ R.H.S
Hence, the answer is prove.