Step-by-step explanation:
We must prove that
cos²a(csc²a-cot²a) = cos²a
If we look at both sides, we can see that we have cos²a * something = cos²a. Therefore, if we can get that something to equal 1, we have our proof. In this case, that something is csc²a-cot²a. Using this information, we can work from within the parenthesis and go from there.
We can start by expanding the items in the parenthesis. Taking that csc(x) = 1/sin(x) and cot(a) = cos(x)/sin(x), we can say that
cos²a(csc²a-cot²a) = cos²a(1/sin²a - cos²a/sin²a). Because both items in the parenthesis have a denominator of sin²a, we can subtract cos²a from 1 to get
cos²a(1/sin²a - cos²a/sin²a)= cos²a((1-cos²a)/sin²a))
Next, we know that cos²a+sin²a=1, so 1-cos²a = sin²a. Plugging that in, we get
cos²a((1-cos²a)/sin²a)) = cos²a(sin²a/sin²a)
= cos²a(1)
= cos²a
Answer:
14, 20, 0, 0, 0
Step-by-step explanation:
The notation indicates the absolute value of x, therefore it can be rewritten as:
if x 0
if x < 0
In this problem, we have the expression
Therefore, we can rewrite it as:
if x ≥ 0:
(a)
If x < 0:
(b)
So now we can substitute the given values into the two expressions:
x = 7 (positive value, so we use expression (a):
x = 10 (positive values, so we use expression (a):
x = 0 (zero, so we can use expression (a):
x = -3 (negative value, so we use expression (b):
x = -8 (negative value, so we use expression (b):
Answer:
0.85 I believe
Step-by-step explanation:
Answer:
18x3 there you go chicken wing it+(
Answer:
Let the age of Aman's son is x years.
So the age of Aman will be 3x years.
Ten years ago, the age of Aman's son = x - 10 and Aman's age = 3x - 10.
So according to question,
5(x - 10) = 3x - 10
or 5x - 50 = 3x - 10
Transposing 3x to the LHS and -50 to the RHS:
5x - 3x = -10 + 50 = 40
or 2x = 40
or x = 20
So Aman's age = 3x = 60 years and
Aman's son's age = x = 20 years.