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 Discussion Forums -> This Post 5 points    (1    in 1 votes )   [?]

Its not cos2A that equals to 2sinAcosA .

sin2A=2sinAcosA

Taking L.H.S

sin2A

sin(A+A)

sinAcosA + sinAcosA

2sinAcosA = R.H.S

Hence proved......

 Discussion Forums -> This Post 10 points    (2    in 2 votes )   [?]

Let A and G be the arithmetic and geometric mean for a, b respectively.

Thn given that, a+b = 6G

(a+b)/2 = 3G

A = 3G

Let  take a quadratic equation in x whose roots are a and b. Then, x^2 - (a+b)x + ab = 0

x^2 - 2Ax + G^2 = 0

Using quadratic formula, we get   x = [2A +- root(4A^2 - 4G^2)] / 2

x = A +- sqrt(A^2 - G^2)

Since a and b are the roots of the then, a = A + sqrt(A^2 - G^2)  & b = A - sqrt(A^2 -G^2)

Then,

Now, putting A = 3G in the above equation we get,

Hence proved.....

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

Find dy/dx if y = cosec^3[root(1+e^{2x})] * root(1+cos2x/sin2x)

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

Find dy/dx if y = sec^2[root(xsinrootx + logx^2)] * ex^3root(1+xsinx)

 This Post 0 points    (0    in 0 votes )   [?]
Hmm..correct
 Discussion Forums -> This Post 5 points    (1    in 1 votes )   [?]

alpha = mC2

= m! / 2! ( m-2)!

= m(m-1)/2

alphaC2 = m(m-1)/2 C 2

 This Post 5 points    (1    in 1 votes )   [?]

As always, VEDIC MATHS TRICKS are always the best. This VEDIC MATHS TRICK will let you do calculations within a few seconds.

This is the trick exclusively applicable to the multiplications of TWO numbers, whose digits at units place add up to 10 as well as whose digit at tenth's place is same. ( Both these conditions must be satisfied.)

For an example, let's take two numbers 83 and 87 ( note that both the above conditions are satisfied, that is, digit at tenth's place is same and at the units place add upto 10 )

1) Firstly, find the product of digits at unit's place, that is, 3*7 = 21

2) Secondly, multiply tenth's place digit by its consecutive number, that is, 8*9 = 72

3) Now finally, your answer is the result in second step followed by the result in first step.

4) Hence, the answer is 7221.

Now, you could do such multiplications orally within few seconds.

 This Post 0 points    (0    in 0 votes )   [?]
Opps!!!sorry. Yes instead on 9, there would be 10. Thanks for the correction.
 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

We know that cos2x = 1-2sin^2x

Let x = 18

then, cos 36 = 1-2sin^2(18)

= 1 - 2(root5 - 1)^2/4^2

= (root5 + 1)/4

and also, we know that

sin36 = root[ 1 - cos^2(36)]

Solving it further, you'll get sin36 = root[ 10 - 2root5] / 4

 Discussion Forums -> This Post 5 points    (1    in 1 votes )   [?]

Equation of the tangent to any ellipse is y = mx + root( a^2m^2 + b^2)      ..........................(1)

Equation of the line through the centre(0,0) to (1) is  y = (-1/m)x       ..............(2)

Eliminating m from (1) and (2), we'll get the required locus of the foot of the perpendicular drawn from the center of the ellipse to any tangent.

You'll get,

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

Wave optics is the branch of optics which studies interference, diffraction, polarization, and other phenomena for which the ray approximation of geometric optics is not valid.

 Discussion Forums -> This Post 5 points    (1    in 1 votes )   [?]

I have got the answer for Ist part. In IInd part, don know where i'm doing the mistake.INSTEAD OF tany, IT MUST BE tanx (acc. to me). So, please let me know whether i m correct or not.

Given, y^2 = secx + tanx

=>   y = (secx + tanx)^0.5

Using the chain rule, dp^n/dx = n p^(n-1) dp / dx

So, putting p = secx + tanx and n = 0.5 , we get

But (secx+tanx)^0.5 = y

Hence,

ysecx/2

=> dy/dx

Hence proved......

 This Post 20 points    (4    in 4 votes )   [?]

Sometimes, while doing caculations we get a biggg number to be multiplied by 9. Its become pretty boring. So for that, here's an enhanced trick for MULTIPLYING A NUMBER BY 9 WITHOUT EVEN TRYING IT.

When you have to multiply a number by 9, simply do the following and you'll have your answer in seconds.

1) Multiply the number the number by 9.

For example, Let the number be 267.

1) Multiplying it by 10, we get 2670.

2) Subtracting the original number the result, that is, 2670 - 267 = 2403

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

An electron always experiences a force in an electric field because that force depends on nothing more than the field strength and the charge.But the force an electron experiences in an magnetic field deppends on VELOCITY. If there is no motion of electron through magnetic field where located, no magnetic force acts.

 Discussion Forums -> This Post 10 points    (2    in 2 votes )   [?]

A Carnot heat engine is a hypothetical engine that operates on the reversible Carnot cycle. A heat engine acts by transferring energy from a warm region to a cool region of space and, in the process, converting some of that energy to mechanical work. The cycle may also be reversed.

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

Adiavatic Process is that process in which no heat enters or leaves the thermodynamic system during the change.

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

In simple words, some materials have the ability to produce electricity when subjected to mechanical stress. This is called the piezoelectric effect.

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

Refer this.................

http://csep10.phys.utk.edu/astr162/lect/light/absorption.html

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]

I think you are asking about electrical polarity. If that's the case then,

Electrical polarity is present in every electrical circuit. Electrons flow from negative pole to positive pole. In a direct current, one pole is always positive and the electrons flow in one direction only. In alternating current circuit, the two poles alternate between negative and positive and the direction of the flow continually reverses.

 Discussion Forums -> This Post 0 points    (0    in 0 votes )   [?]
Thanks......
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