Question

I am stuck on a problem that has to do with the double angle formulas. I have to solve this: 4sinxcosx = 1. I tried using the formula 2sinu = 2sinucosu by substituting it in like this: 2(2sinxcosx)= 1 but then I am stuck

Answer 1

remember that sin 2x = 2sinxcosx

so 4sinxcosx = 1
2(2sinxcosx) = 1
2(sin2x) = 1
sin2x = 1/2

I will assume you are working in degrees, we can always switch later on

so 2x = 30° or 2x = 150° because of the CAST rule
x = 15° or x = 75°

the period of sin 2x is 180°, so adding 180 to any answer will produce new answers

x = 15°, 195°, ...
or
x = 75°, 255°, ...

In Radians:
15° = π/12 radians
x = π/12, 13π/12....
x = 5π/12, 17π/12, ...