cot θ tan (90° -θ) - sec (90° - θ)cosec θ +√3tan 12°tan 60°tan 78° = 2
Consider L.H.S.
= cot θ tan (90° -θ) - sec (90° - θ)cosec θ +√3tan 12°tan 60°tan 78°
= cot θ cot θ - cosec θ cosec θ +√3 tan 60° tan 12° tan 78°
= cot2 θ – cosec2 θ +√3 tan 60° tan 12° tan(90-12)°
= - (cosec2 θ - cot2 θ) +√3 tan 60° tan 12° cot 12°
= - 1 + √3(√3 × tan 12° cot 12°)
= - 1 + √3(√3 × 1)
= - 1 + 3
= 2 = R.H.S.
Hence, proved.