Solve over (0,360) 25 points if anyone can

sec x = 2

sin 2x = cos x

Sec x = 1/cos x = 2===>cos x =1/2===x = 60 deg or π/3

sin 2x = 2sin x cos x = cos x. Divide both sides by cos x ===2sin x =1

& sin x = 1/2 ===> x =30 or π/6

Sec inverse of 2 = x. Meaning it is asking
"Where is sec equal to 2?" Well, sec is one over cos, so we essentially want to know when cos is 1/2. Between 0 and 360 degrees, cos is 1/2 at 60 and 300 degrees.
So your answer is x = 60, and 300

Sin2x=cosx
Use the identity for Sin2x to get:
2sinxcosx = cosx

Now move the cosx over to get:
2sinxcosx-cosx = 0
Take out the greatest common factor:

Cosx(2sinx-1) = 0

Now solve with each individual part.
Cosx= 0
X = 90 and 270 degrees.

2sinx-1 = 0
2Sinx = 1
Sinx = 1/2
X= 30 and 150 degrees.

I hope this Helps!