yoga + vedanta = yoga vedanta

So, what is yoga? what is vedanta? and why to combine them?

INSTRUCTION 3:
This instruction from "moha mudgara" attributed to Sri Anandagiri (A direct disciple of Bhagavan Adi Sankarabhagavadpaada Acharya) as part of the instruction to the old vaiaakarana famously known as bhaja govindam states:

योगरतोवा भोगरतोवा
संगरतोवा संगविहीन
यस्य ब्रह्मणि रमते चित्तं
नन्दति नन्दति नन्दत्येव

yogaratovA bhogaratovA
sangaratovA sangavihIna
yasya brahmaNi ramate chittam
nandati nandati nandatyeva

yoga is about "union" it is opposed to the word bhoga which means "enjoyment"

bhoga means enjoying an external object. This kind of enjoyment is not really enjoyment as it is dependent on the external object. The external object decreases as one continue to consume it. Once the external object is lost the bhoga ends. So bhoga is temporary, dependent and based on external sense organs' capability to acquire and consume this object.

where as

yoga means union of one self with its own true nature. The self's true nature is bliss and once the union is achieved it gives an infinite everlasting bliss and a complete 'transcendental independence' to the one who has attained such a natural and original state.

An individual striving for bhoga on the pravritti maarga will have the tendency to enjoy the sanga (attachment) with similar flocks

where as

an individual striving on the path of yoga will have a tendency to be sangavihina (detached) and alone.

BUT

whose "chittam" rejoices in "brahma" he will enjoy, verily enjoy and ONLY enjoy! He ALONE enjoys the infinite everlasting bliss.
the word nandati is repeated as "nandati nandati" then nandati is qualified with the word "eva" (which means ONLY, ALONE)

Vedanta is all about brahma jignasa - an inquiry into brahman; The vedanta sutras by Sage Baadarayana starts with

अथातो ब्रह्मजिज्ञासा
athAto brahmajiGYAsA BS 1.1.1

and what makes the "chittam" *NOT* rejoice in the brahma (the true awareness of bliss)?
it is called chitta vrittis. The mental and emotional veils that cover the true nature of the self.

Rishi Patanjali defines yoga as:
योगश्चित्तवृत्तिनिरोधः YS 1.2
तदाद्रष्टुःस्वरूपेऽवस्थानम YS 1.3

yogaḥ cittavṛtti nirodhaḥ
tadā draṣṭuḥ svarūpe avasthānam

Hence, the yoga is all about mastering the "chittam" and vedanta is all about inquiry into brahma.

A careful combination of these two (yoga & vedanta) is the safest, surest and well tested path to the everlasting infinite bliss which is the true and original nature of the self!!