Eng. inspire and Sp. inspirar
The cognates Eng. inspire and Sp. inspirar are derived from Lat. inspīrāre, which literally meant ‘to breathe in(to), blow upon (a thing)’, but which had also come to mean ‘inspire’ and ‘excite’, among other things. These two cognates are quite good friends, both meaning primarily ‘fill with the urge or ability to do or feel something’ (COED), a figurative meaning derived from the original figurative sense of the Latin word, as in Eng. His example inspired us all and Sp. Su ejemplo nos inspiró a todos (VOX).
Eng. inspire has a second, related meaning whose synonym is encourage, which does not translate into Spanish as inspirar but rather as estimular or animar, as in What happened to her inspired her to work harder = Sp. Lo que sucedió la animó a esforzarse más. Eng. inspire is also used with complements such as fear, respect, and confidence. The preferred translation of this sense of Eng. inspire is infundir or suscitar, not so much inspirar, if the inspired feeling is a negative one, as in infundir miedo ‘to inspire fear’. Finally, the Spanish verb inspirar is often used in the reflexive form, inspirarse (en), which translates as to be inspired (by) or to draw inspiration (from).
We should mention that some dictionaries tell us that Eng. inspire and Sp. inspirar can also mean ‘to inhale’, even though that is not what the source word meant in Latin and even though they are rarely used that way. The DLE even gives that as the first (!) sense for the word inspirar (English dictionaries that mention this sense, always mention it last and usually they mention that is a technical sense). This is quite odd indeed, for it is very rare for these words to be used with that sense, other than in a literary, technical, or otherwise affected context. More common than inspirar for this sense are respirar (para adentro) (equivalent to to take a breath in English) and inhalar ‘to inhale’, especially when something other than air is involved.
As we saw earlier, the noun derived from this verb inspīrāre was inspīrātĭo inspīrātĭōnis, the source of Eng. inspiration and Sp. inspiración. Lat. inspīrātĭo was a Late Latin creation, which meant pretty much what its descendants mean today and was thus derived from the ‘inspire’ sense of the verb inspīrāre. Old English borrowed this noun first in the 12th or 13th centuries and it passed on to English and Spanish in the following centuries.
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 The cognates Eng. inhale and Sp. inhalar are loanwords from Lat. inhālāre ‘to breathe upon’, derived from hālāre ‘to breathe out, emit as breath’ by means of the prefix in‑ that added the meaning ‘into, in, within; on, upon; towards, against’ (as opposed to the other in‑ prefix in Latin, the negative one, the one that is cognate with Eng. un‑, cf. Part I, Chapter 5)