If `0ltalphaltpi/4` then the range of `cosec 2alpha-cot 2alpha` is (A) (0,1) (B) `[1,oo)` (C) `RR` (D) `[0,oo)`

If 0ltalphaltpi/2, show that alpha- alpha^3/3ltsinalpha

If expression x^2-4cx+b^2gt0 for all x epsilon R and a^2+c^2ltab then range of the function (x+a)/(x^2+bx+c^2) is (A) (0,oo) (B) (0,oo) (C) (-oo,oo) (D) none of these

The range of the function f(x)=|x-1| is A. (-oo,0) B. [0,oo) C. (0,oo) D. R

If cos alpha=(5)/(13) and 0 lt alpha lt 90^(@) , then the value of cot alpha+"cosec "alpha is

If sinalpha=5/13 and pi/2ltalphaltpi then the value of (secalpha+ tan alpha)/(cosec alpha - cot alpha)

Show that 1+cot^2alpha/(1+cosecalpha)=cosec alpha

Consider the quadratic equation x^2-mx+1=0 with two roots alpha and beta such that alpha + beta =m and alpha beta =1 The values of m for which alphalt1 and betagt1 are (A) [-2,oo[ (B) [-2,2] (C) [2,oo] (D) ]-oo,-2]

Range of f(x) =sin^20x+cos^48x is (A) [0,1] (B) (0,1] (C) (0,oo) (D) none of these

If the equation x^(3)+bx^(2)+cx+1=0,quad (b

If 1+sin^(2)alpha=3sin alpha cos alpha , then values of cot alpha are (a) -1,1, (b) 0,1, (c) 1,2, (1) -1,1