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sveticcg [70]
3 years ago
9

Can someone please answer. There is one problem. There's a picture. Thank you!

Mathematics
1 answer:
AveGali [126]3 years ago
3 0
Using SOH, the answer is O/H therefore is b/a.
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Which of the following is equivalent to tan2θcos(2θ) for all values of θ for which tan2θcos(2θ) is defined?
Aloiza [94]

Answer:

2sin²θ - tan²θ

Step-by-step explanation:

Given

tan²θcos(2θ)

Required

Simplify

We start by simplifying cos(2θ)

cos(2θ) = cos(θ+θ)

From Cosine formula

cos(A+A) = cosAcosA - sinAsinA

cos(A+A) = cos²A - sin²A

By comparison

cos(2θ) = cos(θ+θ)

cos(2θ) = cos²θ - sin²θ ----- equation 1

Recall that cos²θ + sin²θ = 1

Make sin²θ the subject of formula

sin²θ = 1 - cos²θ

Substitute sin²θ = 1 - cos²θ in equation 1

cos(2θ) = cos²θ - (1 - cos²θ)

cos(2θ) = cos²θ - 1 +cos²θ

cos(2θ) = cos²θ + cos²θ - 1

cos(2θ) = 2cos²θ - 1

Substitute 2cos²θ - 1 for cos(2θ) in the given question

tan²θcos(2θ) becomes

tan²θ(2cos²θ - 1)

Open brackets

2cos²θtan²θ - tan²θ

------------------------

Simplify tan²θ

tan²θ = (tanθ)²

Recall that tanθ =  sinθ/cosθ

So, we have

tan²θ = (sinθ/cosθ)²

tan²θ = sin²θ/cos²θ

------------------------

Substitute sin²θ/cos²θ for tan²θ

2cos²θtan²θ - tan²θ becomes

2cos²θ(sin²θ/cos²θ) - tan²θ

Open bracket (cos²θ will cancel out cos²θ) to give

2(sin²θ) - tan²θ

2sin²θ - tan²θ

Hence, the simplification of tan²θcos(2θ) is 2sin²θ - tan²θ

Option E is correct

7 0
3 years ago
The frequency table below shows the antenna careers among the incoming class of first-year college students. Every student is ch
neonofarm [45]

To solve this you must use a proportion like so...

\frac{part}{whole} = \frac{part}{whole}

The total number of students that can be chosen are 4,663. This number will represent the whole of one fraction in the proportion. We want to know what percent probability out of these students are engineer, medical doctor/surgeon. This would be considered the part of this fraction. Sum the number of engineering students (615) with medical doctors/surgeons (723) to find this number

723 + 615 = 1,338 students that want to be an engineer or medical doctor/surgeon

Percent's are always taken out of the 100. This means that the other fraction in the proportion will have 100 as the whole and x (the unknown) as the part.

Here is your proportion:

\frac{1,338}{4,663} =\frac{x}{100}

Now you must cross multiply

1,338*100 = 4,663*x

133,800 = 4,663x

To isolate x divide 4,663 to both sides

133,800/4,663 = 4,663x/4,663

28.7 = x

This means that there is a 28.7% of a student with the intent of becoming an engineer or a medical doctor/surgeon to be chosen at random

Hope this helped!

~Just a girl in love with Shawn Mendes

8 0
3 years ago
Read 2 more answers
Hey! Please help me
mafiozo [28]

Answer:

Exact: 10.08

To 1 decimal place: 10.1

Step-by-step explanation:

Just ask.

Hope this helps.

3 0
3 years ago
Twenty customers bought the portable drill when it was on sale. Twelve of
vekshin1

Answer:

x+y = t

Step-by-step explanation:

7 0
3 years ago
What is the solution for f(n)=1.25n+6.25; 25???<br> Please answer this quickly
gogolik [260]
It would be f= 1.25n+6.25/n
                

8 0
3 years ago
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