If m = (cos θ – sin θ) and n = (cos θ + sin θ) then show that

Given: m = (cos θ – sin θ)

n = (cos θ + sin θ)

Now, =

Multiply numerator and denominator by cos θ – sin θ :

Therefore, =

=

Now, =

Multiply numerator and denominator by cos θ + sin θ :

Therefore, =

=

Now, consider =

=

=

=

Divide numerator and denominator by cos θ:

=

=

Therefore, =

Hence, proved.