# Tutor profile: Anmol G.

## Questions

### Subject: Trigonometry

Prove that cos2x = cos$$ ^{2}$$x - sin$$ ^{2}$$x = 1 - 2sin$$ ^{2}$$x = 2cos$$ ^{2}$$x - 1 from cos(A+B) = cosA cosB - sinA sinB.

cos2x = cos(x+x) cos(x+x) = cosx cosx - sinx sinx = cos$$ ^{2}$$x -sin$$ ^{2}$$x .................. ( 1 ) From eq. ( 1 ) cos$$ ^{2}$$x - sin$$ ^{2}$$x = cos$$ ^{2}$$x - ( 1 - cos$$ ^{2}$$x ) { since, sin$$ ^{2}$$x = 1 - cos$$ ^{2}$$x } = cos$$ ^{2}$$x - 1 + cos$$ ^{2}$$x = 2cos$$ ^{2}$$x - 1 ....................... ( 2 ) Again from eq. ( 2 ) cos$$ ^{2}$$x - sin$$ ^{2}$$x = ( 1 - sin$$ ^{2}$$x ) - sin$$ ^{2}$$x { since cos$$ ^{2}$$x = 1 - sin$$ ^{2}$$x } = 1 - 2sin$$ ^{2}$$x ......................... ( 3 ) Thus from eq. ( 1 ) , ( 2 ) and ( 3 ) cos2x = cos$$ ^{2}$$x - sin$$ ^{2}$$x = 1 - 2sin$$ ^{2}$$x = 2cos$$ ^{2}$$x - 1

### Subject: Basic Math

If the polygon with the least number of sides is a triangle then the polygon with the maximum number of sides will be??

Take a triangle, join two of them side by side you will get a quadrilateral, join five of them together, you will going to get a pentagon, join one more you will get a hexagon. Keep on adding triangles you will get heptagons, octagons and so on... After joining n number of triangles together, you will end up making a circle. Thus, the polygon with the maximum number of sides is nothing but a circle.

### Subject: Physics

State the difference between impulse and momentum.

When a moving body of mass 'm' has a velocity 'v' , it is said to have gained some momentum which is the product of the mass of the body and its velocity Thus, Momentum = m*v Momentum can also be considered as the quantity of motion of a body. When talking about impulse, as the definition says, " it is the rate of change of momentum ". Coming to the meaning part, Suppose a body of mass 'm' is travelling with a velocity 'v' and due some external or internal force applied for a time $$ \triangle t$$, there was a change in its velocity, its momentum will also change. Thus impulse can also be considered as the force applied on a moving body for a certain time duration. thus, Impulse = F*$$ \triangle t$$ = m*$$ \triangle v$$

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