Question

(cosx-sinx)=? and (cosx+sinx)=?

Answer 1

1} [1/sec(x) - 1/cosec(x) ] = cosec(x)-sec(x)
2} [1/sec(x) + 1/cosec(x) ] = cosec(x)+sec(x)

Answer 2

here this answer



cosx−sinxcosx+sinx= 
=[cosx−sinxcosx+sinx]cosx+sinxcosx+sinx]=
=cos2x−sin2x(cosx+sinx)2=
Apply trig identities:
cos2x−sin2x=cos2x
(cosx+sinx)2=cos2x+2sinx.cosx+sin2x=1+sin2x
Finally,
cosx−sinxcosx+sinx=cos2x1+sin2x



I HOPE IT IS HELPFUL TO YOU