Which is a multiple of 5 17,532,235 or 48 ?
2 answers:
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Answer:
L.S = R.S ⇒ Proved down
Step-by-step explanation:
Let us revise some rules in trigonometry
- sin²α + cos²α = 1
- sin2α = 2 sin α cosα
- cscα = 1/sinα
To solve the question let us find the simplest form of the right side and the left side, then show that they are equal
∵ L.S = csc2α + 1
→ By using the 3rd rule above
∴ L.S = + 1
→ Change 1 to
∴ L.S = +
→ The denominators are equal, then add the numerators
∴ L.S =
∵ R. S =
∵ (sinα + cosα)² = sin²α + 2 sinα cosα + cos²α
∴ (sinα + cosα)² = sin²α + cos²α + 2 sinα cosα
→ By using the 1st rule above, equate sin²α + cos²α by 1
∴ (sinα + cosα)² = 1 + 2 sinα cosα
→ By using the 2nd rule above, equate 2 sinα cosα by sin2α
∴ (sinα + cosα)² = 1 + sin2α
→ Substitute it in the R.S above
∴ R. S =
∵ L.S = R.S
∴ csc 2α + 1 =
Answer:
Step-by-step explanation:
Recall that one needs just three points on the plane to determine the form of the quadratic function that goes through them, because a quadratic function is defined by three parameters. We therefore can pick just three simple ones that facilitate our calculations.
Realize that we need to find the parameters and
that gives as a function of the form:
that satisfies the values given in the table.
The simplest point to start with is the point (0,-6) which means that when x is 0 (zero), the value of y must be "-6". Placing such values in the general form, renders what the value of the parameter "c" should be:
So parameter must be "-6".
Now let's use other simple values of "x" that facilitate our calculations, and include the value we just found, to reduce the number of unknowns:
point (1, 2):
Point (-1, -20):
Now, we can add these two equations term by term as they are, in order to get rid of the unknown "b":
So we just found the value for parameter "" = -3
Now we can use it as well as c = -6 in one of the equations we reduced above, in order to find the parameter (b) that we are missing:
So now we have the three parameters we need to define the quadratic function:
You can also check that the other points given in the table (2, 4) a,d (3, 0) are indeed points that belong to this quadratic function.
Step-by-step explanation:
Hence, option D is the correct answer.