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Step-by-step explanation:

Given If tan^2 alpha= cos^2 beta-sin^2beta, then prove cos^2alpha-sin^2alpha= tan^2 beta

We need to know the formula

cos2x = 1 - tan^2 x /1 + tan ^2 x

cos2x = cos^2 x - sin ^2 x

Now it is given

tan ^2 alpha = cos^2 beta - sin^2 beta

tan^2 alpha = cos2 beta

tan^2 alha = 1 - tan^2 beta / 1 + tan^2 beta

By componendo and dividendo we get

1 - tan^2 alpha/1 + tan^2 alpha = 1 + tan^2 beta - (1 - tan^2 beta) / 1 + tan^2 beta + 1 - tan^2 beta

cos2 alpha = 2 tan^2 beta / 2

tan^2 beta = cos^2 alpha - sin^2 alpha

Here from vendiagram

n(a-b) =n(a)-n(anb)

And, n(b-a) =n(b)-n(anb)

Again from vendiagram we get 1 formula

n(aub)=n(a-b)+n(b-a)+n(a-b)

n(aub)=n(a)+n(b)-n(anb) [putting the value of n(a-b), n(b-a) ]

Hence proved.

thanks

A is a subset of B, then every element of A is an element of B. We need to prove that A union B = B. This is an equality of sets, so we must prove that every element of each set must be in the other set.

Suppose x is in B. Then clearly x is in A union B. Suppose x is in A union B. Then x is in A or x is in B. If x is in B, we are done. If x is in A, then since A is a subset of B, x is also in B. Either way, x is in B, and we are done. Therefore A union B = B.

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c)C+38°28'=90°00' C=89°60'-38°28' C=51°32' . . .

a)C+81°=90°C=9°

b)C+47°=90°C=90°-47°=43°

It will be 0as cos 67° = sin 23socos ²67-cos²67=0

balanced equation is an equation for a chemical reaction in which the number of atoms for each element in the reaction and the total charge are the same for both the reactants and the products. ... Also Known As: Balancing the equation, balancing the reaction, conservation of charge and mass..

On 1st Jan,She saved 10 Rs. Next Day 11 Rs. Next Day 12 rs

So money saved by her= 10 + 11 + 12 + 13 + .........................+ (till 31st Dec)

Now, Above Sum is the sum of a Arithmetic Progression witha = 10d = 1n = 366 ( since year 2016 is a Leap Year)

=>Sum of an A.P. = (n/2){ 2a + (n-1)d} = (366/2){ 20 + 365 } = 70455

So, she saved Rs. 70455 till the end of the year

Hit like if you find it useful!

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CP= Rs 800,Profit % =4%, loss%=12%

To find SP when CP and Profit% is known

SP = [(100 + Profit%) / 100]×CP

=((100+4)/100)×800

=(104/100)* 800

=Rs 832

ER. RAVI KUMAR ROY..

To find SP when CP and Loss % is known

SP = [(100 – Loss %) / 100]*CP

=((100-12)/100)*800

=(88/100)*800

=Rs 704

Total CP=Rs 1600

Total SP= Rs 832+ 704 = 1536

SP of 1 watch = 1536/2 = Rs768

Loss on both the watch= CP-SP=1600 -1536= Rs 64

Prof Samuelson pointed correctly that Robbins’ definition is not dynamic in nature, because it has only discussed about the problems of present generation, not anything about future generation. Hence the definition suffers with the problem of economic growth.

by BODMAS rule1/5+3/20-2/7=(28+21-40)/140=9/140

thankd

Given: A+B=90Sin(A+B)=Sin 90=1Now, LHS=Sin²A+Cos²A =Sin²90+Cos²90 =(1²)+(0²) =1 =RHS

sorry im mistaken with the question... il post another answer

A+B=90sin(A+B)=sin90=1LHSsin^2A+cos^2A= sin^290+ cos^2 90= (1)^2+(0)^2= 1+0= 1=RHS

CP = 800.Profit = 6 2/3 %SP = (100+ 20/3)/ 100 * 800= 320/3 * 8= Rs. 853.33

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SP of total agricultural field at a profit of 10% = (360000*110)/100 = Rs. 396000.

So, SP of 1/3 of field = (360000/3)*(80/100) = Rs. 96000.

SP of 2/5th of the field =(2*360000*125)/(5*100) = Rs. 180000.

Hence,

SP of the remaining field = Rs. (396000-96000-180000).

= Rs. 120000.

Cost of the land = Rs 72,000

Find the expected selling price to gain 10%:

10% gain = 10% x 72,000 = 0.1 x 72,000 = Rs 7,200

Expected selling price = 72000 + 7200 = Rs 79,200

Find the Selling Price of the 1/3 of the land sold at 20% loss:

cost of 1/3 of the land = 1/3 x 72,000 = Rs 24,000

20% loss = 20% x 24,000 = 0.2 x 24000 = Rs 4800

Selling Price = 24,000 - 4800 = Rs 19,200

Find the selling price of the 2/5 land that gains 25%:

Cost of the 2/5 land = 2/5 x 72000 = Rs 28,800

25% gain = 25% x 28,800 = 0.25 x 28800 = Rs 7200

Selling Price = 28,800 + 7200 = Rs 36,000

Find the selling price of the remaining land:

Selling Price = 79,200 - 19,200 - 36,000 = Rs 24,000

Answer: The selling price of the remaining land is Rs 24,000

72000*1/3=24000*(100-20)%=19200.2/5*72000=28800*125%=36000.he have to make a profit of 72000* 10%=7200, 72000+7200- ( 19200+36000)=24000. so remainingland sold at Rupees 24000.

The selling price of the remaining land is Rs.24,000please like my answer

the selling price 24000

Patriotism is the feeling and expression of love for one’s home country, along with a feeling of unity with those who share those feelings

It is feeling to be proud on country

Patriotismor national pride is the feeling of love, devotion and sense of attachment to a homeland and alliance with other citizens who share the same sentiment. This attachment can be a combination of many different feelings relating to one's own homeland, including ethnic, cultural, political or historical aspects.

Patriotismor national pride is the feeling of love, devotion and sense of attachment to a homeland and alliance with other citizens who share the same sentiment. This attachment can be a combination of many different feelings relating to one's own homeland, including ethnic, cultural, political or historical aspects.

It is the feeling and expression of love for one's home country

Patriotismor national pride is the feeling of love, devotion and sense of attachment to a homeland and alliance with other citizens who share the same sentiment. This attachment can be a combination of many different feelings relating to one's own homeland, including ethnic, cultural, political or historical aspects.

Patriotismor national pride is the feeling of love, devotion and sense of attachment to a homeland and alliance with other citizens who share the same sentiment. This attachment can be a combination of many different feelings relating to one's own homeland, including ethnic, cultural, political or historical aspects.

patriotism is a felling to be sacrificed

Forests sometimes contain many tree species within a small area (as in tropical rain and temperate deciduous forests)

I want one word answer not detail or description of answer

Let the coordinates of the point be (0,y) and y-axis divides the line segment in the ratio k :1.

(0,y) = {(10k-4)/k+1 ,(12k-6)/k+1}

0=10k-4/k+1

10k =4

k=2/5 ==>the ratio of division is 2:5

now, y =(12k-6)/k+1

y={(12*2/5) -6}/(2/5)+1

y =-6/7

thus the coordinates of the point is (0,-6/7)

500 ks 10% badhne par 50 rs badh kar 550 rs ho jayega. fir 550 ka 10% ghatane par 55 rs ghatega aur betan 495 rs ho jayega. ( b) 495 Rs

B) is the correct answer

a correct answer is (b) 495

For question 28.a + 5d =0a=-5d (1)now LHS,a + 32 d = (32 - 5) d from (1)= 27dRHS,3(a + 14 d) = (14d - 5d) 3 = 9 x 3 d= 27d

LHS = RHSHence proved.

2*2+(-1)*(-3)=7 iska answer ho sakta h

We know that the section formula

The point which divide the line segment

joining the points A ( x1 , y1 ) , B ( x2 , y2 ) in the ratio k:1

is P ( kx2+ x1/k +1 , ky2 + y1 / k+ 1 )

______________________________________________

According to the given problem ,

A( x1 , y1 ) = ( 1/2 , 3 /2 )

B ( x2 , y2 ) = ( 2 , -5 )

P ( x , y ) = ( 3 / 4 , 5 / 12 )

Let the ratio = k : 1

x = 3/4 ( given

(kx2 + x1 ) / ( k+ 1 ) = x

( k× 2 + 1/2 ) / ( k + 1 ) = 3 / 4

2k + 1/2 = 3 /4 ( k + 1 )

4 ( 2k + 1 / 2) = 3 ( k + 1 )

8k + 2 = 3k + 3

8k - 3 k = 3 - 2

5k = 1

k = 1/5

Therefore ,

Required ratio = k : 1

= 1 /5 : 1

= 1 : 5

P divides the line segment joining the piints A and B

in the ratio 1 : 5

is it 100%correct

√4030+0+4060225+1√40642562016

4(3y+1)=2(7y-5)12y+4=14y-1012y-14y=-10-4-2y=-14y=7

The ratio is 1/3 because the volume of cone is one third of the volume of cylinder as depicted by the formulae.

wrong

x^2-5=(x+root(5))(x-root(5))so zeroes are root(5),-root(5)

The domain is all the x points (x,y)

so, domain is from -2 to 2

and range is all the y points range = [1,4]

also you can see that the points representthe function y =x²

and for the domain [-2,2]

its range is [0,4]

Let ABC is an equilateral ∆ whose each side =x units. O be the circumcenter

and OA=OB=OC= r. Draw OD perpendicular on BC. Now BD=BC/2=x/2.

In right ∆ ODB

BD/OB=cos30°

or. (x/2)/r=√3/2

or. x/r=√3

or. x=√3.r

or. Side of an equilateral ∆ = √3 × Circumradius of that ∆.

sum of 2 no is 33.

= 1st no = 18.another no is 33-18=15.ans=15.check 18+15=33