Question

prove that tanhx/sechx-1+tanhx/sechx+1=-2cosechx​

Answer 1

Answer:

Step-by-step explanation:

As we know that

sec  

2

x−tan  

2

x=1,

Or

sec  

2

x=1+tan  

2

x,                  ......(1)

Or

sec  

2

x−1=tan  

2

x                  ......(2)

Given that:

sec  

4

x−sec  

2

x=tan  

4

x+tan  

2

x

LHS=sec  

4

x−sec  

2

x

=sec  

2

x(sec  

2

x−1)

=(sec  

2

x)(tan  

2

x)                       [From equation (2)]

RHS=tan  

4

x+tan  

2

x

=tan  

2

x(tan  

2

x+1)

=(tan  

2

x)(sec  

2

x)                       [From equation (1)]

=(sec  

2

x)(tan  

2

x)

Hence, LHS=RHS.

Answer 2

Answer:

prove that tanhx/sechx-1+tanhx/sechx+1=-2cosechx