Given,

Consider, a=b=1

=

=

=

Now, cosx=A (cosx+sinx) +B (cosx+sinx)

=A (cosx+sinx) +B (-sinx+cosx)

Equating ’cosx’ coeff:- Equating ‘sinx’ coeff:-

1=A+B 0=A-B

A=B

1=A+A

2A=1

A=1/2 B=1/2

[since,

(x)+