Proof

Question 1

Proof sin2x using additional formula

Question 2

Proof cos2x using additional formula

Question 3

Proof tan2x using additional formula

Question 4

Show that cos3x=4cos^3(x) - 3cosx

Question 5

Show that sin3x = 3sinx - 4sin^3(x)

Question 6

Using first principles show cos0 = -sin0

Question 7

Using first principles show sin0= cos0

Question 8

Using quotient rule show that d/d0 (tan0) = sec^2(0)

Question 9

Show that the derivative of a^x is a^x ln(a)

Question 10

Show that the integration of ln(x) = xln(x) - x + c

Question 11

Show thta intergrayion of sin^2(x) = x/2 - sin2x/4 + c

Question 12

Show thta the integration of cos^2(x) = sin2x/4 + x/2 + c

Question 13

Prove by contradictiom that square root of 2 is an irrational number

Question 14

Prove that there are infinitely many primer numbers

Question 15

Prove that the sum of the first n terms of an arithmetic series is n/2[2a +(n-1)d]

Question 16

A geomatric series has first term a and common ratio r. Prove that sum of the first n terms in this series is given by sn=a(1-r^n)/1-r

Question 17

Derive
V=u+ at

Question 18

Derive
S=1/2(u+v)t

Question 19

Derive
S= ut + 1/2at^2

Question 20

Derive
S=vt - 1/2at^2

Question 21

Derive
V^2= u^2 +2as

Question 22

Show that
Time of flight = 2Usina/g

Question 23

Show that
Grastdst hieght= u^2 sin^2(a)/2g

Question 24

Show that
Range on horizontal plane= U^2sin2a/g

Question 25

Show that Equatiom lf trajectory: y = xtana - gx^2(1+ tan^2(a))/2U^2