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.