cos 255

since cos 255=cos (180+75)
=cos 75
=cos (45+30)
=(cos45)*(cos 30)-(sin45)*(sin 30) (ucing expansion of cos(c+d))
=(1/sqrt(2))*(sqrt(3)/2)-(1/sqrt(2))*(1/2)
=(1/2sqrt(2))*(sqrt(3)-1)

Solution steps

2sin(sq)x = sinx
=>2sin(sq)x - sinx = 0
=>sinx(2sinx -1) =0
=>sinx=0 or (2sinx -1) = 0

since(0<= x <= 2(pi))
for sinx=0
x= 0,pi,2(pi)
for sinx = (1/2)
x= pi/6 or (5/6)pi

so x=0, pi/6, pi, (5/6)pi, 2(pi)


plz...let me know how much was I upto the mark...

venn

a = 28 (car pools) (red)

b = 31 (took buses) (orange)

c = 42 (drove to school) (yellow)

d = 9 (car pools and buses) (a meets b)

e = 10(used car pools and sometimes their own cars) (a meets c)

f = 6 (used buses as well as their own cars) (b meets c)

g = 4 (used all three methods) (all 3 meet)

*Remember all d,e,f involves region g

rest all calculations are simple

1.How many students use none of the three methods?

u-(a+b+c-d-e-f+g) = 100-((28+31+42)-9-10-6+4) = 20

2.How many students use car pools exclusively to get to school?

a-(d+e-g) = 28-(9+10-4) = 13 g \\ as g is repeated twice so we subtract g\\

3.How many students use buses exclusively to get to school?

b-(d+f-g) = 31-(9+6-4) = 20 \\ as g is repeated twice so we subtract g\\

Botany

It is a Branch of Biology dealing with scientific study of plant life and developement