# By ..., one yields...?

In a scientific context I have a sentences of the form

By doing ..., we yield ...

Now, I am trying to neutralize it to something like

By doing ..., one yields ...

Unfortunately, I cannot find this formulation anywhere else. Is it a valid formulation anyway?

Example:

By multiplying the equation with (x+1) and applying standard solving techniques for ODE, [one yields/we yield] the identity sin²(x) + cos²(x) = 1.

• Yield means roughly “to result in” or “to become as a result”. If you perform some calculation, you are not resulting in anything, and therefore do not yield anything. The calculation is, and does. Neither of your sentences is good English, though they are both perfectly comprehensible. May 13, 2014 at 16:02
• "If you perform some calculation, you are not resulting in anything" why not? May 14, 2014 at 11:42
• Because that is not what yield means. Just like equals is something the sums of a calculation do, not something you do. You don't say, “Adding two plus four, I equal six” any more than you say, “Adding two plus four, I yield six”. You say, “Two plus four yields/equals six”. May 14, 2014 at 13:11

This use of "yield" sounds a little off to me. Usually, "to yield" meaning "to produce" is applied to things or processes:

the farm yields 20,000 kilos of tomatoes,

but not people:

*the farmer yields 20,000 kilos of tomatoes     (unidiomatic).

So I would use one of the following:

Multiplying the equation by (x+1) and applying standard solving techniques for ODEs yields the identity.

or

By multiplying the equation by (x+1) and applying standard solving techniques for ODEs, we obtain the identity.

Multiplying the equation with (x+1) and applying standard solving techniques for ODE yields the identity sin²(x) + cos²(x) = 1.

or

The identity sin²(x) + cos²(x) = 1 is yielded by multiplying the equation with (x+1) and applying standard solving techniques for ODE.

'Yields' sounds a bit airy-fairy. Why not simply:

Multiplying the equation by (x+1) and applying standard solving techniques for ODEs gives us the identity sin²x + cos²x = 1.

or

We obtain the identity sin²x + cos²x = 1 by multiplying the equation by (x+1) and applying standard solving techniques for ODEs.

Recrystallisation yielded (or 'resulted in a yield of') one million tons by mass of a mystical substance which induces feelings of serenity on contact.

i.e. action yielded result(s)