If coshα=secx, then tan2x2=?
cos2α2
sin2α2
cot2α2
tanh2α2
Find the value of tan2(x2):
Given, coshα=secx
As we know that,
coshα=eα+e-α2=secx
Also we know that, tanh2(α2)=[eα2-e-α2eα2+e-α2]2
=eα+e-α-2eα+e-α+2=2secx-22secx+2=secx-1secx+1=1cosx-11cosx+1=1-cosx1+cosx=1-1-2sin2x21+2cos2x2-1=sin2x2cos2x2=tan2x2
∴tan2(x2)=tanh2(α2)
Hence, Option ‘D’ is Correct.