tan2x*cotx - 3 = 0
We know that: tan2x = sin2x/cos2x and cotx = cosx/sinx
==> sin2x/cos2x *cosx/sinx = 3
Now we know that sin2x = 2sinx*cosx
==> 2sinxcosx/cos2x * cosx/sinx = 3
Reduce sinx:
==> 2cos^2 x/ cos2x = 3
Now we know that cos2x = 2cos^2 x-1
==> 2cos^2 x/(2cos^2 x -1) = 3
==> 2cos^2 x = 3(2cos^2 x -1)
==> 2cos^2 x = 6cos^2 x - 3
==> -4cos^2 x= -3
==> 4cos^2 x = 3
==> cos^2 x = 3/4
==> cosx = +-sqrt3/ 2
<span>==> x = pi/6, 5pi/6, 7pi/6, and 11pi/6</span>
Because the 18-gon is symmetrical, you can rotate it by 360/18 or 20 degrees. This is because when you rotate it by 20 degrees(to the left for explanation matters), any angle will now be in the position of its angle to its left.
Answer:
percentage change= 500%
Step-by-step explanation:
After diet the weight reduced = 30 pounds
Before diet her weight = 180 pounds
percentage change = { (180 - 30) ÷ 30 } × 100
= ( 150 ÷ 30) × 100
= 5 × 100
= 500 %
∴percentage change= 500%
