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Ghella [55]
3 years ago
11

Simplify the expression. Quantity cosecant of x to the power of two times secant of x to the power of two divided by quantity se

cant of x to the power of two plus cosecant of x to the power of two.
A. sin^2x
B. cos^2x
C. -1
D. 1
Mathematics
1 answer:
Art [367]3 years ago
3 0

Answer:

D. 1

Step-by-step explanation:

We have the expression, \frac{\csc^{2}x\sec^{2}x}{\sec^{2}x+\csc^{2}x}

We get, eliminating the cosecant function,

\frac{\sec^{2}x}{\frac{\sec^{2}x}{\csc^{2}x}+1}

As, sinx is reciprocal of cosecx and cosx is reciprocal of secx,

i.e. \frac{\sec^{2}x}{\frac{\sin^{2}x}{\cos^{2}x}+1}

i.e. \frac{1}{\cos^{2}x}\times \frac{\cos^{2}x}{\sin^{2}x+\cos^{2}x}

Since, we know that, \sin^{2}x+\cos^{2}x=1

Thus,

\frac{1}{\cos^{2}x}\times \frac{\cos^{2}x}{\sin^{2}x+\cos^{2}x}=1

So, after simplifying, we get that the result is 1.

Hence, option D is correct.

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>First jump = 4.25 m

 

>Best jump = 1.12 * First jump

Best jump = 1.12 * (4.25 m)

Best jump = 4.76 m

 

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Hence,

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Answer:

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Step-by-step explanation:

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Sphinxa [80]

Answer:

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Step-by-step explanation:

first, we would set up an equation. let 3x-4 represent "four less than a number tripled". "a number" would be represented by x. let x+10 represent "the same number increased by 10".

set 3x-4 and x+10 equal to each other:

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then, we would get the 2x by itself. we would do this by adding 4 to both sides:

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finally, we would divide each side of the equation by 2 to find x:

x=7.

The number is 7.

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