Answer:
D
Step-by-step explanation:
our basic Pythagorean identity is cos²(x) + sin²(x) = 1
we can derive the 2 other using the listed above.
1. (cos²(x) + sin²(x))/cos²(x) = 1/cos²(x)
1 + tan²(x) = sec²(x)
2.(cos²(x) + sin²(x))/sin²(x) = 1/sin²(x)
cot²(x) + 1 = csc²(x)
A. sin^2 theta -1= cos^2 theta
this is false
cos²(x) + sin²(x) = 1
isolating cos²(x)
cos²(x) = 1-sin²(x), not equal to sin²(x)-1
B. Sec^2 theta-tan^2 theta= -1
1 + tan²(x) = sec²(x)
sec²(x)-tan(x) = 1, not -1
false
C. -cos^2 theta-1= sin^2
cos²(x) + sin²(x) = 1
sin²(x) = 1-cos²(x), our 1 is positive not negative, so false
D. Cot^2 theta - csc^2 theta=-1
cot²(x) + 1 = csc²(x)
isolating 1
1 = csc²(x) - cot²(x)
multiplying both sides by -1
-1 = cot²(x) - csc²(x)
TRUE
7. Straight lines are also = to 180°
If you look at the diagram, when you add the two angles together, they form a straight line.
Since the angles add up to 180°, you can do:
(x + 25)° + (4x + 5)° = 180°
x + 25 + 4x + 5 = 180 Combine like terms
5x + 30 = 180 Subtract 30 on both sides
5x = 150 Divide 5 on both sides
x = 30
Actually, distributive property isn't needed to combine this. You can simply subtract 7 from 13 which will give you 6. The solution is 6c.
