Consider L.H.S.

= cosec (65° + θ) — sec (25° —θ) — tan (55° — θ) + cot (35° + θ)

= cosec (65° + θ) — sec (90° - (65° + θ)) — tan (90° - (35° + θ)) + cot (35° + θ)

= cosec (65° + θ) — cosec (65° + θ)) — cot (35° + θ) + cot (35° + θ)

= 0 = R.H.S.

Hence, proved.