E-Store[himanshu] for my dear goiitians...shortcuts
well frnz , here it goes , some useful shortcuts in trigo etc....
it will help u in cbse also for checking ur answer....
HOPE U LIKE IT
1) The value of
sin(pi/14).sin(3pi/14).sin(5pi/14).sin(7pi/14).sin(9pi/14).sin(11pi/14).sin(13pi/14)
here's the shortcut
value = 1 / 2n -1
n = no. of terms
so ans = 1/64
condition (standardization shud be there).........(denomenator shud be even)
2)The value of cos(2pi/15).cos(4pi/15).cos(8pi/15)cos(14pi/15)
shortcut
ans = 1/2n
ans = 1/16
condition (den. must be odd)
3)The angle fr cos@ = tan@
is 2 sin 18 degrees
4)Sin(pi/7) + sin(2pi/7) + sin(3pi/7)
shortcut
value = 1/2 cot (1/2 (first or smallest angle))
= 1/2 cot ( (1/2).(pi/7))
= 1/2 cot (pi/14)
condition ----angle must be in series.... (pi 2pi 3pi etc)
5)and in sin qs if denomenator is odd
sin (pi/7).sin(2pi/7).sin(3pi/7)
shortcut
= (denomenator)1/2 / 2n
= root7 / 8
its the ans
Functions
f(x) = x3 + 5
then f-1(x) = ????????
simple yaar
y = x3 + 5
y - 5 = x3
now just interchange x and y
x - 5 = y3........................this is the major step
i.e (x - 5)1/3 = y
matrices
trace of a matrix ---add the elements of primary diagonals....
1.....-5.....7
0.....7......9
11....8.....9
trace = 1 + 7 + 9 = 17
its the ans
hope these helps
cheers!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Comments (19)
thanksssssssssssssssss!!!!!!!!!!!!!!!!!!!!
sin(pi/14).sin(3pi/14).sin(5pi/14).sin(7pi/14).sin(9pi/14).sin(11pi/14).sin(13pi/14)
here's the shortcut
value = 1 / 2n -1
n = no. of terms
so ans = 1/64
can u pls explain i find ki there r 7 no.of terms from sin(pi/14) to sin(13pi/14)
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