D. csc^2 x + sec^2 x = 1
The process for each option is to rewrite the equation, attempting to obtain the identity sin^2 x + cos^2 x = 1. In general convert each function to its equivalent using just sin and cos.
A. cos^2 x csc x - csc x = -sin x
cos^2 x * 1/sin x - 1/sin x = -sin x
(cos^2 x * 1/sin x - 1/sin x) * sin x = -sin x * sin x
cos^2 x * 1 - 1 = -sin^2 x
cos^2 x = -sin^2 x + 1
cos^2 x + sin^2 x = 1
Option A is an identity.
B. sin x(cot x + tan x) = sec x
sin x(cos x/sin x + sin x/cos x) = 1/cos x
cos x + sin^2 x/cos x = 1/cos x
cos^2 x + sin^2 x = 1
Option B is an identity.
C. cos^2 x - sin^2 x = 1- 2sin^2 x
cos^2 x - sin^2 x + 2sin^2 x = 1- 2sin^2 x + 2sin^2 x
cos^2 x + sin^2 x = 1
Option C is an identity.
D. csc^2 x + sec^2 x = 1
1/sin^2 x + 1/cos^2 x = 1
cos^2 x/(cos ^2 x sin^2 x) + sin^2 x/(cos^2 x sin^2 x) = 1
(cos^2 x + sin^2 x)/(cos ^2 x sin^2 x) = 1
1/(cos ^2 x sin^2 x) = 1
1 = cos ^2 x sin^2 x
Option D is NOT an identity.
Hey there!
To find the answer, we can divide the total cost by the total number of juice boxes.
A half of a dollar is 50 cents.
Thus, each juice box cost 50 cents.
Have an awesome day! :)
Answer:
B. If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, the triangles are congruent.
Step-by-step explanation:
The definition of Hypotenuse-Leg Theorem is stated in option B . In the picture attached, an example is given.
Rational number thats the answer
Using a system of equations, it is found that there are 10 baskets that hold 4 meals in the shop.
<h3>What is a system of equations?</h3>
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given by:
- Variable x: Number of baskets that hold 2 meals.
- Variable y: Number of baskets that hold 4 meals.
There are 25 baskets in the shop, hence:
x + y = 25 -> x = 25 - y
They can hold a total of 70 meals, hence:
2x + 4y = 70
2(25 - y) + 4y = 70
2y = 20
y = 10
There are 10 baskets that hold 4 meals in the shop.
More can be learned about a system of equations at brainly.com/question/24342899
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