Find all solutions to the equation in the interval [0, 2π).

cos x = sin 2x

pi divided by two., three pi divided by two.
pi divided by six., pi divided by two., five pi divided by six., three pi divided by two.
0, π
0, pi divided by six, five pi divided by six., π

x = π/6, π/2, 5π/6, 3π/2

Step-by-step explanation:

cos x = sin(2x)

Use double angle formula.

cos x = 2 sin x cos x

Move everything to one side and factor.

cos x − 2 sin x cos x = 0

cos x (1 − 2 sin x) = 0

Set each factor to 0 and solve.

cos x = 0

x = π/2, 3π/2

1 − 2 sin x = 0

sin x = 1/2

x = π/6, 5π/6

The total solution is:

x = π/6, π/2, 5π/6, 3π/2

sas (side angle side)

aa (angle angle)

sss(side side side)

sas find two sides with an angle in between

aa is finding two angles and the third will add up to 180

sss find all sides

step-by-step explanation:

but which class are u may know that first