Consider the L.H.S.
=tan(3π4+θ)tan(π4+θ)
We know that,
tan(A+B)=tanA+tanB1−tanAtanB
Therefore,
=⎛⎜ ⎜ ⎜⎝tan3π4+tanθ1−tan3π4×tanθ⎞⎟ ⎟ ⎟⎠⎛⎜ ⎜⎝tanπ4+tanθ1−tanπ4×tanθ⎞⎟ ⎟⎠
Since,
tan3π4=−1
tanπ4=1
Therefore,
=(−1+tanθ1+tanθ)(1+tanθ1−tanθ)
=(−1+tanθ1−tanθ)
=−(1−tanθ1−tanθ)
=−1
R.H.S
Hence, proved.