All categories

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

What is the following 2/ √13 + √11

Korvikt [17]

Answer:

Its C

Step-by-step explanation:

4 0

4 years ago

How many students must be randomly selected to estimate the mean weekly earnings of students at one college? We want 95% confide

kari74 [83]

Answer:

The sample of students required to estimate the mean weekly earnings of students at one college is of size, 3458.

Step-by-step explanation:

The (1 - α)% confidence interval for population mean (μ) is:

$CI=\bar x\pm z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}$

The margin of error of a (1 - α)% confidence interval for population mean (μ) is:

$MOE=z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}$

The information provided is:

σ = $60

MOE = $2

The critical value of z for 95% confidence level is:

$z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

Compute the sample size as follows:

$MOE=z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}$

$n=[\frac{z_{\alpha/2}\times \sigma }{MOE}]^{2}$

$=[\frac{1.96\times 60}{2}]^{2}$

$=3457.44\\\approx 3458$

Thus, the sample of students required to estimate the mean weekly earnings of students at one college is of size, 3458.

8 0

3 years ago

The slope of EF¯¯¯¯ is −5/2 .

stellarik [79]

Answer:

LM and NP

Step-by-step explanation:

LM= 2/5

NP=2/5

GH= -5/2

JK= =5/2

4 0

3 years ago

How to do this 24:96 = 5:?

Rama09 [41]

Um... I think you meant 24:96 = 5:x

In that case, x=20

6 0

3 years ago

20 = 7x + 2 - 4x What does x equal

saveliy_v [14]

Answer:

x = 6

Step-by-step explanation:

20 = 7x + 2 - 4x

7x + 2 - 4x = 20 (switch the sides)

7x - 4x + 2 = 20 (group the like terms together)

3x + 2 = 20 (add similar numbers, in this case it's the both x's)

-2 -2 (subtract 2 on both sides)

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

3x = 18

/3 /3 (divide both sides by 3)

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

x = 6

5 0

2 years ago

Read 2 more answers

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

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