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 formequate 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 formequate 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 formequate 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 formequate 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