Finding an identity to solve cos ⁡ t − 2 cos ⁡ ( 2 t...

Keenan Santos

Keenan Santos

Answered

2022-07-11

Finding an identity to solve cos t 2 cos ( 2 t ) = 0

Answer & Explanation

toriannucz

toriannucz

Expert

2022-07-12Added 16 answers

One option is to rewrite the second term using the double angle identity
cos 2 t = 2 cos 2 t 1 ,
which gives the equation
cos t 2 ( 2 cos 2 t 1 ) = 0.
Expanding (and canceling a sign for presentation) gives
4 cos 2 t cos t 2 = 0 ,
which is a quadratic in cos t, so it can be analyzed using the Quadratic Formula.

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