Expressing acoshx +bsinhx in The Form Rcosh(x+-alpha) or R sinh(x+-alpha)
The identities(1) and
(2) will be useful here.
To expressin the form
equate both expressions and expand the right hand side using identity (1)
Equate coefficients of
(1)
and coefficients of
(2)
(1) divided by (2) gives
andgives
To expressin the form
equate both expressions and expand the right hand side using identity (1)
Equate coefficients of
(3)
and coefficients of
(4)
(3) divided by (4) gives
andgives
To expressin the form
equate both expressions and expand the right hand side using identity (2)
Equate coefficients of
(5)
and coefficients of
(6)
(6) divided by (5) gives
andgives
To expressin the form
equate both expressions and expand the right hand side using identity (2)
Equate coefficients of
(7)
and coefficients of
(8)
(8) divided by (7) gives
andgives