Proof of cos 2x = cos²x - sin²x = 2cos²x - 1 = 1 - 2sin²x = (1 - tan²x) /(1 + tan²x)

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In this tutorial you will learn the proof of the a very important trigonometric identities:
cos 2x = cos²x - sin²x = 2cos²x - 1 = 1 - 2sin²x = (1 - tan²x) /(1 + tan²x)
where x is not an odd multiple of pi/2.
These can also be written as
cos 2θ = cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2sin²θ = (1 - tan²θ) /(1 + tan²θ)
where θ ≠ (2n + 1) π/2, n is an integer
or
cos 2theta = cos²theta - sin²theta = 2cos²theta - 1 = 1 - 2sin²theta = (1 - tan²theta) /(1 + tan²theta)
where theta ≠ nπ +π/2, where n is an integer.
00:00 About it
00:26 Proof of cos 2x = cos²x - sin²x
01:21 Proof of cos 2x = cos²x - sin²x = 2cos²x - 1
02:03 Proof of cos 2x = cos²x - sin²x = 2cos²x - 1 = 1 - 2sin²x
02:26 Proof of cos 2x = (1 - tan²x) /(1 + tan²x)
04:38 Why angle x cannot be odd multiple of pi/2?
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[@dntaneja5137]

Quite interesting derivation.

[@brahmachari1]

Nice explanation sir