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We have
.If
In the same way if one of the others two factors from (1) is 0
Find the acute angles a and b that satisfy the following simultaneous equations:
2sin 2b =3 sin 2a
tan b =3 tan a
Find the positive integers n for which n^3+1 and n^2-1 are both divisible by 101
how many non overlapping 2 by 2 squares will fit into a circle with radies 8
PLESE step by step
but how JaneFairfax
Find real solutions of the system
sin x + 2 sin(x+y+z) = 0,
sin y + 3 sin(x+y+z) = 0,
sin z + 4 sin(x+y+z) = 0.
Prove that for every natural n the following inequality is valid:
|sin 1| + |sin 2| + |sin(3n-1)| + |sin(3n)| > 8n/5.
sum Series
1/(log 2) + 1/(log 2)(log 3) + 1/(log 2)(log 3)(log 4) + ...
1/(sin²1)² + 1/(sin²1+sin²2)² + 1/(sin²1+sin²2+sin²3)² + 1/(sin²1+sin²2+sin²3+sin²4)² + .
these four numbers must equal 24 3,3,7,7 you can use add. sub. mul. div. each number must only be used once
Find the last decimal digit of the sum 1^1 + 2^2 + 3^3 + ... + 2001^2001
Triangle ABC is not isosceles. The incenter is I, the excenter is O. The incircle touches the sides BC, CA, AB at points D, E, F, respectively. Lines FD and AC intersect at P, lines DE and AB intersect at Q. The midpoints of segments EP amd FQ are M and N, respectively. Prove that MN and OI are perpendicular.
(4,9).is the only answer but how
A circle with center O and radius 1 cm rolls around the inside of a triangle whose sides are 6, 8, and 10 cm, always touching one or more of the sides as it rolls. How far does O travel in one complete circuit?
n positive integers
prove
solve in R
JaneFairfax you are jenus
using the addition formula for tangents, we have
.Now obviously, for t = pi/7, 2pi/7, ..., 7pi/7, we have
. and thus, these are the roots of .Put differently,
. are the roots of .Since
JaneFairfax you are jenus
using the addition formula for tangents, we have
.Now obviously, for t =\ pi/7, 2\pi/7, ..., 7\pi/7, we have
. and thus, these are the roots of .Put differently,
. are the roots of .Since
. , we may divide by x to leave an equation of which. are the roots: .a,b,c,d integers, a+b+c+d=0
prove
a^5+b^5+c^5+d^5 divisible by 10
cos (-89)+cos (-87) +.......+cos87 +cos 89 =csc 1
tan²(pi/7) +tan²(2pi/7) +tan²(3pi/7) =21
solve
x + y^2 + z^3 = 3
y + z^2 + x^3 = 3
z + x^2 + y^3 = 3