Posted by **Solly** on Tuesday, May 10, 2011 at 2:48am.

Cos70cos10+sin70sin10 e =2cos^2 2x-1

- Maths -
**Reiny**, Tuesday, May 10, 2011 at 7:24am
Cos70cos10+sin70sin10 e =2cos^2 2x-1

don't know what that "e" is supposed to be, seems to be superfluous.

recall : cos (A-B) = cosAcoB + sinAsinB

Cos70cos10+sin70sin10 =2cos^2 2x-1

cos(70-10) = 2cos^2 2x - 1

cos60 = 2cos^2 2x - 1

recall cos 2A = 2cos^2 A - 1

so 2cos^2 2x - 1 = cos 4x

cos 4x = cos60

4x = 60° or 4x = 300°

x = 15° or x = 75°

since cos 2x has a period of 180°

other solutions would be

x = 15+180 = 195°

or

x = 75+180 = 255°

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