Math, asked by kalaitrick, 8 months ago

8.
Prove that cosh-¹x = log(x+√x²-1)​

Answers

Answered by dayaparmarparmar866
1

Step-by-step explanation:

Let

y

=

cosh

1

x

then by definition

x

=

cosh

y

=

e

y

+

e

y

2

2

x

=

e

y

+

e

y

e

y

2

x

+

e

y

=

0

e

y

2

x

+

1

e

y

=

0

e

2

y

2

x

e

y

+

1

=

0

Let

u

=

e

y

then we have

u

2

2

x

u

+

1

=

0

--> Now use quadratic formula to solve

u

=

2

x

±

4

x

2

4

2

e

y

=

2

x

±

4

x

2

4

2

e

y

=

2

x

±

4

(

x

2

1

)

2

2

e

y

=

2

x

±

2

x

2

1

e

y

=

x

±

x

2

1

ln

e

y

=

ln

(

x

±

x

2

1

)

y

=

ln

(

x

+

x

2

1

)

cosh

1

x

=

ln

(

x

+

x

2

1

)

Answered by khushiism800
2

Answer:

letx= cosh x

log e = 1

log e^(u) = u log e

put the valureof sin hx and cos hx

sinhx = 1/2 (e^x- e^-x)

coshx = 1/2 ( e^x + e-^x)

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