log tan(π÷4+x÷2)=2tanh-¹(tan x÷2)
Answers
Answered by
5
Step-by-step explanation:
Given, u=logtan(
4
π
+
2
θ
)
tanh(
2
u
)=
cosh(
2
u
)
sinh(
2
u
)
=
e
2
u
+e
−
2
u
e
2
u
−e
−
2
u
=
tan(
4
π
)+
cot(
4
π
+
2
θ
)
tan(
4
π
+
2
θ
)
−
cot(
4
π
+
2
θ
)
=
tan(
4
π
+
2
θ
)+cot(
4
π
+
2
θ
)+2×(
tan(
4
π
+
2
θ
)cot(
4
π
+
2
θ
)
)
tan(
4
π
+
2
θ
)−cot(
4
π
+
2
θ
)
[multiply denominator and numerator by
tan(
4
π
+
2
θ
)
+
cot(
4
π
+
2
θ
)
]
=
sin(
2
π
+θ)
2
+2
sin(
2
π
+θ)
−2cos(
2
π
+θ)
=
1+sin(
2
π
+θ)
−cos(
2
π
+θ)
=
1+cosθ
sinθ
=
2cos
2
2
θ
2sin
2
θ
cos
2
θ
tanh(
2
u
)=tan
2
θ
[sinx=2sin
2
x
cos
2
x
,cos2x=2cos
2
x−1]
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