1)
LHS = cot(a/2) - tan(a/2)
= (1 - tan^2(a/2))/tan(a/2)
= (2-sec^2(a/2))/tan(a/2)
= 2cot(a/2) - cosec(a/2)sec(a/2)
= 2(1+cos(a))/sin(a) - 1/(cos(a/2)sin(a/2))
= 2 (1+cos(a))/sin(a) - 2/sin(a)) (product to sums)
= 2[(1+cos(a) -1)/sin(a)]
=2cot a
= RHS
2.
LHS = cot(b/2) + tan(b/2)
= [1 + tan^2(b/2)]/tan(b/2)
= sec^2(b/2)/tan(b/2)
= 1/sin(b/2)cos(b/2)
using product to sums
= 2/sin(b)
= 2cosec(b)
= RHS
Answer:
19 cents or 0.199
Step-by-step explanation:
Hope it helped!
70 / 35 = 2
So the 70 pound dog weights double the weight of the 35 pound dog, so he will eat twice as much.
2 x 2.5 = 5 cups
Meaning he will eat 5 cups of dry dog food a day.
By the same logic a 140 pound dog would have to eat twice what a 70 pound dog eats, that is 10 cups of dry dog food a day, so 7 1/2 cups are not enough.
Challenge: per pound a dog eats more than a cat. Since you know a 140 pound dog eats 10 cups, you can dive 140 by 10, to find out that each cup feeds 14 pounds, so half a cup would be the amount of food to feed a 7 pound dog, meaning that a dog weighing 1 pound less than a 8 pound cat would need the same amount of food, so it eats more than a cat.
1.330
2.930
3.30
4.80
5.90
6.140
7.10
8.110
Answer:
The use of symbols to represent ideas or qualities.
