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2 years ago

Sin2A+Sin2B÷Sin2A-Sin2B=Tan(A+B)÷Tan(A-B) Prove that

Mathematics

1 answer:

igor_vitrenko [27]2 years ago

8 0

Take L.H.S sin2A+sin2B/sin2A-sin2B

= sin2A+sin2B/sin2A-sin2B

Put

[sinC+sinD = 2sin(C+D)/2cos(C-D)/2]

[sinC-sinD = 2cos(C+D)/2.sin(C-D)/2]

= 2 sin(2A+2B)/2 cos(2A-2B)/2 / 2 cos(2A+2B) sin(2A-2B)

= sin(A+B).cos(A-B)/cos(A+B).sin(A-B)

= sin(A+B)/cos(A+B) . cos(A-B)/sin(A-B)

= tan(A+B).cot(A-B)

= tan(A+B).1/tan(A-B)

= tan(A+B)/tan(A-B)

∴ Hence we proved sin2A+sin2B/sin2A-sin2B=tan(A+B)/tan(A-B)

You might be interested in

Of the people who prefer mocha, the relative frequency of them preferring it cold is

WITCHER [35]

Answer

1) Relative frequency of prefering cold mocha amongst mocha drinkers = 0.32

2) Relative frequency of prefering a latte amongst hot coffee drinkers = 0.22

3) Type of coffee that has the highest percentage of people who prefer it cold = Regular

Explanation

1) Relative frequency of prefering cold mocha amongst mocha drinkers is given as

Relative frequency

= (Number of mocha drinkers who prefer it cold) ÷ (Total number of mocha drinkers)

Number of mocha drinkers who prefer it cold = 12

Total number of mocha drinkers = 12 + 25 = 37

Relative frequency = 12 ÷ 37 = 0.32

2) Relative frequency of prefering a latte amongst hot coffee drinkers is given as

Relative frequency

= (Number of latte drinkers who prefer it hot) ÷ (Total number of hot coffee drinkers)

Number of latte drinkers who prefer it hot = 19

Total number of hot coffee drinkers = 11 + 25 + 19 + 30 = 85

Relative frequency = (19/85) = 0.22

3) Percentage of people who prefer cold coffee for each coffee type

Regular

(17/28) = 60.7%

Mocha

(12/37) = 32.4%

Latte

(20/39) = 51.3%

Cappuccino

(27/57) = 47.4%

Regular coffee drinkers have the highest percentage of drinkers who prefer it cold.

Hope this Helps!!!

7 0

1 year ago

Ruth and Juan Dimas would like yo borrow $2,600 for 90 days to pay their real estate tax. State savings and Loan charges 7.25 pe

steposvetlana [31]

Answer:

$2647.13

$2648.08

Step-by-step explanation:

To solve for the value of each loan we will use the formula:

$A=P(1+rt)$

Let's break down the variables that we have.

P = $2,600

r = 7.25% or 0.0725

r2 = 7.50% or 0.0750

t = 90 days

Now since we're computing for two different types of interest, let's take it one at a time.

First the State Saving and Loan.

In this situation we are solving for ordinary interest, where we compute with the total number of days are 360

$A=P(1+rt)$

$A=2,600(1+(0.0725)(\dfrac{90}{360})$

$A=2,600(1+(0.0725)(0.25)$

$A=2,600(1+0.018125)$

$A=2,600(1.018125)$

$A=2,647.13$

The maturity value of State Savings and Loan is $2,647.13.

Now let's move on to the Security bank.

The security bank charges 7.5% exact interest. For exact interest we use 365 days.

$A=2,600(1+(0.0750)(\dfrac{90}{365})$

$A=2,600(1+(0.0750)(0.246575)$

$A=2,600(1+(0.0184931)$

$A=2,600(1.0184931)$

$A=2,648.08$

The maturity value of the Security bank is $2,648.08.

5 0

4 years ago

How do u estimate 368+231

vlabodo [156]

Answer:

You round 368 to 370 and 231 to 230. Then you add and get 600

Step-by-step explanation:

8 0

4 years ago

Read 2 more answers

A math test has 24 problems on it. If a student incorrectly answers 3 problems on the test, what percentage of problems are corr

GenaCL600 [577]

Answer:

they would get somewhere from 80% to 85%

Step-by-step explanation:

7 0

3 years ago

WILL GIVE BRAINLISEST!

____ [38]

If polygons are similar ratio if sides will be same

$\\ \sf\longmapsto \frac{x}{50} = \frac{48}{40} \\ \\ \sf\longmapsto 40x = 48 \times 50 \\ \\ \sf\longmapsto x = \frac{48 \times 50}{40} \\ \\ \sf\longmapsto x = \frac{2400}{40} \\ \\ \sf\longmapsto x = 60$

3 0

3 years ago

Sin2A+Sin2B÷Sin2A-Sin2B=Tan(A+B)÷Tan(A-B) Prove that​

Sin2A+Sin2B÷Sin2A-Sin2B=Tan(A+B)÷Tan(A-B) Prove that