Prateek

Please show me the steps

Please show me the steps

Please show the working.

The answer is: 7 pi - 20.

Our sir said that, sin^-1 (sin x) = 3 pi - x, and, cos^-1 (cos x) = 4 pi - x.

I didn't understand the reason.

Please explain. Thanks.

sinx cosx = (1/2) 2 sinx cosx = (1/2) sin (2x)

Integral = (1/2) (-(1/2) cos (2x)) + C

= -(1/4) cos (2x) + C

Also, sinx cosx dx = sinx d (sinx)

Integral = (1/2) sin^2 (x) + C

So, -(1/4) cos (2x) = (1/2) sin^2 (x)

Or, -cos (2x) = 2 sin^2 (x)

But this is not true. Where did I make the mistake?

y^(y^(y^(y^(... to infinity = ln (x + ln (x + ln (x + ... to infinity

Find dy/dx.

dy/dx can contain both x and y terms.

x+x+x+x+.... (upto x terms) = x^2

Differentiate both sides with respect to x.

1+1+1+1+... (upto x terms) = 2x

Or, x = 2x

Question: Find the ratio in which the line segment formed by joining (2, 4, 5) and (3, 5, 4) is divided by the y-z plane.

My solution: Let the ratio be m:n and P be the point of intersection of the line and the plane. The x-coordinate of P must be zero.

So, (3m + 2n) / (m+n) = 0 which gives,

m:n = -2:3 (there is a negative sign before 2)

But the answer given in the book is 2:3.

It might be a silly question but I'm learning 3D coordinate geometry for the first time. Please explain me the solution. Thanks in advance.

It is written in the book that, increase in temperature will shift the reaction towards endothermic.

Endothermic means heat is absorbed and exothermic means heat is released. If temperature increases then to undo the effect the reaction should shift towards exothermic to release the added heat.

Where am I making the mistake?

1. Toluene → p. Toluidine

2. Toluene → p. Toluic acid

3. acetone → propane

Answer given in the book: (abc)^(1/3).

I have understood recently how a clutch works. But my question is, why do we need it? I searched in google and they say that, the engine is always rotating but not the wheels. How is that possible? When the car is being driven, the wheels are rotating. I can't understand the importance of clutch. Any explanation would be appreciated. Thanks.

I have some knowledge about the different parts of a car and how they work. I have seen one thing:

Suppose the car is at rest and I change to first gear. Then I slowly take my foot up (which is on the clutch). After a time the car starts moving. I keep holding the clutch at that point. The car keeps going (very slowly though). Same thing happens with the back gear.

How does it happen? I don't press the accelerator. Also, is it safe to do so every time?

Suppose I'm driving a maruti alto or swift at a speed 50 to 80 kmph at 4th gear. Now I remove my foot from the accelerator and change the gear to neutral.

Recently my friend told me that I shouldn't do that. I shouldn't keep the gear at neutral when the car is moving. First I should stop the car then make the gear neutral.

Is it true? I mean if I don't do that then how can that harm my car?

Show that, cosA cosC = 2 (c^2 - a^2) / (3ca)