Project ForgeEngineering Mathematics
Calculus
GATE 2013
Medium
Choose the CORRECT set of functions, which are linearly dependent.
- Asin x, sin²x and cos²x
- Bcos x, sin x and tan x
- cos 2x, sin²x and cos²x
- Dcos 2x, sin x and cos x
Explanation
The double-angle identity cos2x = cos²x − sin²x gives 1·cos2x − 1·cos²x + 1·sin²x = 0, a non-trivial linear combination equaling zero — so cos2x, sin²x, and cos²x are linearly dependent. None of the other option sets satisfy such an identity.
Source: GATE ME 2013 (Booklet Code A) (2013)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.