How to solve this half angle identities

90° ⩽ x ⩽ 180° is another way of saying that the angle "x" is in the II Quadrant, where sine is positive whilst cosine is negative, as you can see in your Unit Circle.  We also know that csc(x) = 2, so

now, the angle "x/2" is half the arc of the angle "x", and since the angle "x" is in the II Quadrant, we can conclude the half of that arc will be on the I Quadrant, where sine and cosine and tangent are all positive.

width of rectangle in terms of x =  ( x + 0.5)

Area of rectangle =372

Length of rectangle = 15.5

Step-by-step explanation:

Given that,

Length of rectangle = 2x² + 9x + 4

Area of rectangle = x + 4

To find,

width of rectangle

Formula of area of rectangle

2x² + 9x + 4 = x + 4 * width

2x² + 9x + 4 / ( x + 4) = width

solving the quadratic equation in numerator to find the factors

x = -4 and x = -0.5

( x + 4 )( x + 0.5) / (x + 4) = width

canceling (x + 4) from numerator and denominator

( x + 0.5) = width

So the width of rectangle in terms of x = ( x + 0.5)

suppose width of rectangle = 12

then,

( x + 0.5) = 12

x = 11.5

Area of rectangle = 2x² + 9x + 4

= 2(11.5)² + 9(11.5) + 4

= 372cm

length of rectangle = x + 4

= 11.5 + 4

= 15.5cm