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Find the minimum value of 4sin^(2)x+4cos...

Find the minimum value of `4sin^(2)x+4cos^(2)x` .

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CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. If a ,b , a n dc are distinct positive real numbers such that a+b+c=1,...

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  2. Prove that b^2c^2+c^2a^2+a^2b^2> a b cxx(a+b+c)(a ,b ,c >0) .

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  3. Find the minimum value of 4sin^(2)x+4cos^(2)x .

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  4. Prove that (a b+x y)(a x+b y)>4a b x y(a , b ,x ,y >0)dot

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  5. The minimum value of the sum of real number a^-5,a^-4,3a^-3,1,a^8 and ...

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  6. If a1,a2,------ ,an are positive real numbers whose product is a fixe...

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  7. If a ,b ,c ,d are positive real umbers such that a+b+c+d=2,then M=(a+...

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  8. A straight line through the vertex P of a triangle P Q R intersects th...

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  9. If alpha in (0,pi/2), then sqrt(x^2+x)+tan^2alpha/sqrt(x^2+x) is alw...

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  10. In A B C , prove that cos e c A/2+cos e c B/2+cos e c C/2geq6.

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  11. In Delta A B C , prove that t a n A+t a n B+t a n Cgeq3sqrt(3),w h e...

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  12. If a ,b ,c are real numbers such that 0 < a < 1,0 < b < 1,0 < c < 1,a+...

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  13. If a^2+b^2+c^2=x^2+y^2+z^2=1, then show that a x+b y+c z leq1.

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  14. Prove that a^4+b^4+c^4> a b c(a+b+c),w h e r ea ,b ,c > 0.

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  15. Prove that the greatest value of x y is c^3/sqrt(2a b), if a^2x^4+b^2y...

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  16. If a > b and n is a positive integer, then prove that a^n-b^n > n(a b)...

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  17. If y = sin^-1(10x) + pi/2 then find the value of dy/dx .

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  18. If a+b=1,a >0, prove that (a+1/a)^2+(b+1/b)^2geq(25)/2dot

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  19. If Cr=(n !)/([r !(n-r)]), the prove that sqrt(C1)+sqrt(C2)+.......sq...

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  20. If x and y are positive real numbers and m, n are any positive integ...

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