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Andrews [41]
2 years ago
13

Simplify sin^2y/sec^2 y−1 to a single trigonometric function

Mathematics
1 answer:
liubo4ka [24]2 years ago
6 0

Answer:

\frac{ { \sin}^{2} y}{ { \sec}^{2}y - 1 }  =  { \cos }^{2} y

Step-by-step explanation:

We know that { \tan }^{2} y =  { \sec }^{2} y - 1

Also , { \tan}^{2} y =   \frac{ { \sin }^{2} y}{ { \cos }^{2}y }

So ,

\frac{ { \sin }^{2}y }{ { \sec }^{2}y - 1 }  =  \frac{ { \sin}^{2} y}{ { \tan }^{2} y}  =  \frac{ { \sin }^{2}y }{ \frac{ { \sin}^{2} y}{ { \cos}^{2}y } }  =  { \cos }^{2} y

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Taye recruits two people to be election campaign volunteers. The next week he ask each of those volunteers to recruit two more c
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Using a geometric sequence, it is found that:

a) For the first 5 weeks, the numbers are: 2, 4, 8, 16, 32

b) Hence some of the volunteers can stop recruiting new volunteers during the 7th week.

<h3>What is a geometric sequence?</h3>

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

a_n = a_1q^{n-1}

In which a_1 is the first term.

For this problem, on the first week there are 2 people, and since each new people involve two more, the common ratio is of 2, hence the parameters for the geometric sequence are:

a_1 = 2, q = 2

Hence the number of people after n weeks is:

a_n = 2 \times 2^{n - 1}

For the first 5 weeks, the numbers are:

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There will be 150 volunteers when a_n = 150, hence:

2 \times 2^{n - 1} = 150

2^{n-1} = 75

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The above is because 2^7 = 128 and 2^8 = 256, and 128 < 150 < 256.

Hence some of the volunteers can stop recruiting new volunteers during the 7th week.

More can be learned about geometric sequences at brainly.com/question/11847927

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