One of the prominent password-resetting options of any website or service, Instagram included, is to reset your account password using the email address on file. In addition to your standard password reset method, Instagram provides its users with a secondary method to reset a password by using your Facebook account. If you previously synced both your Facebook and Instagram accounts together, you can use your Facebook account to access your Instagram account and reset the password. You can reset your password via Facebook only when using Instagram on a mobile device.
Tap the "Forgot Password?" link on the sign in screen and tap the "Reset using Facebook" button.
Type your Facebook username and password and tap "Log In."
Enter a new password in both the "New Password" fields and tap "Reset" to reset your Instagram password using Facebook.