If `x=log_e[tan(pi/4+theta/2)]` then `cos hx=`

If x = log [ tan (pi/4 + theta/2 ) ] then cosh x =

If x=log_(e)[cot((pi)/(4)+theta)] then sin hx=

If x=log_e tan(pi/4+theta/2) then prove that (i) tanh(x/2)=tan(theta/2) and (ii) cos theta* cos hx=1

If theta in ((-pi)/(4), (pi)/(4)) and x=log_(e )[cot((pi)/(4)+theta)] then prove that (i) cosh x= sec 2theta" " (ii) sinh x=-tan 2theta

If u=log_(e )"Tan"((3pi)/(4)+(theta)/(2)) then coshu=

If x is an acute angle and y=log_(e)[tan((pi)/(4)+(x)/(2))] then cosh x*cosh y