1. given:
csc(x) + sin(x)
2. definition of csc(x) :
1/sin(x) + sin(x)
3. combining fractions with a common denominator:
(1 + sin²(x))/sin(x)
4. expanding 1 = cos²(x) + sin²(x) :
(cos²(x) + sin²(x) + sin²(x))/sin(x)
5. simplifying:
(2 sin²(x) + cos²(x))/sin(x)
6. employing the same identity as in (4) :
(2 (1 - cos²(x)) + cos²(x))/sin(x)
7. expanding 2 (1 - cos²(x)) :
(2 - 2 cos²(x) + cos²(x))/sin(x)
8. simplifying:
(2 - cos²(x))/sin(x)
This is 10.5^2 10.5 is the base and 2 is the exponent. The area is 110.25 square inches.
The sum of all three angles in any triangle is always 180 degrees. So in obtuse triangle there is only one obtuse angle (more than 90 degrees). If we have for example an obtuse angle of 91 degrees, then two other angles have to fit in 89 degrees which makes it impossible for any of them to be obtuse.
1) Area = (b*h)/2 = (9*5)/2 = 45/2 = 22.5 (Letter A)
2) Area = b*h = 8*14 = 112 (Letter D)
3) Surface area of a prism is SA=2B+ph (B = area of the base, p = perimeter of the base, h = height)
B = 15 * 5 = 75 cm^2
p = 15 + 5 = 20 cm
SA = 2*75 + 20*7 = 150 + 140 = 290 (G)
4) V = (B*H*L)/2 = (15*7*5)/2 = 525/2 = 262.5 cm^3 (G)
5) V = 9^3 = 81 cm^3 worth of wrapping (A)
6) V = (B*H*L)/2 = (13*6*8)/2 = 312 cube feet (J)
It gave me ADGGAJ. I don't know if this is right, but I atleast tried to do something, right?
The solution is x=6 and y=5
