Sending an Equip Card you control to the GY is a cost to activate the effect.
You can send a Trap Card like "Kunai with Chain" that is equipped to a monster as the cost to activate the effect to destroy 1 card.
If you Special Summoned "Evocator Chevalier" with "Symbols of Duty" and then send "Symbols of Duty" to the GY as a cost, "Evocator Chevalier" will still destroy 1 card your opponent controls.
If the effect of "Evocator Chevalier" is active due to "Supervise" and you send "Supervise" to the GY as a cost to activate the effect of "Evocator Chevalier", you still destroy 1 card your opponent controls.