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If a , b , c are a triangle angles, prove : csc(a/2)+csc(b/2)+csc(c/2)≥6 ...
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1 + 2 + 3 + 4 +......+ n ≥ (n+n^2)/2 ...
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Show that infinete series Σ sin( 1/k ) is div? ...
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Find ∫ ( 1/x6 + 1/x8 )1/3dx i.e integrate cubic root of (1/x6+1/x8) ...
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find ∫ x3-2/ (x3+1)3 dx ...
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If A is an Invertible Matrix, Show that det(AT A)>0 ...
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Show that: cos( π/7 )cos( 2π/7 )cos( 3π/7 )= 1/8 ...
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Find the smallest value for the function : f(x) = |x-2| + |x+3| + |x-4| ...
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If a , b and c are angles in triangle such cot a + cot b + cot c = √3 prove that abc is an equalitial triangle. ...
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Let x,y be two nonzero real numbers with a,b real show that : a2| x/y |+b2| y/x |≥2ab ...
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If x,y>0 show that : 1/x+y < 1/x + 1/y ...
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C1,C2 and C3 are 3 tangent circles, these circle tangent to a line too. If the radius of C1 is 9 and radius of C2 is 4. Find the raduis of c3. ...
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If h(x)= 10/x -2 find directly h-1(2) ...
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Solve the equation : cos2x + cos22x + cos23x = 1 for all x ...
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If x , y , z are three real numbers not equal to 1 such that xyz=1 show that : x2/(x-1)2 + y2/(y-1)2 + z2/(z-1)2 ≥1 ...
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If a,b,c and d are real positive such that : a + b + c + d = 1 Show that : 4a+1 + 4b+1 + 4c+1 + 4d+1 < 6 ...
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Sorry. Mistakes that the question repeated ...
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Let a , b , c possitive real numbers : Show that : a/(b+c)2 + b/(c+a)2 + c/(a+b)2 ≤ 9/4(a+b+c) ...
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Show that : sin5x+cos5x+sin4x≤2 for all values of x, ...
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Determine all pairs (a,b) of positive integer such : a2/2ab2-b3+1 positive integer ...
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If x,y,z≥0 and x2+y2+z2=3 Find the max for the expression F=xy+xz+yz+ 5/x+y+z ...
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Show that : tan2 π/7 +tan2 2π/7 +tan2 3π/7 =21 ...
