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

Verify : "cosec "alpha=1+cot^(2)alpha" if "alpha=(pi)/(3) .

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

Let A (0,2),B and C be points on parabola y^(2)+x +4 such that /_CBA (pi)/(2) . Then the range of ordinate of C is (a) (-oo,0)uu (4,oo) (b) (-oo,0] uu[4,oo) (c) [0,4] (d) (-oo,0)uu [4,oo)

8. 1+sin^(2)alpha=3sin alpha cos alpha ,then values of cot alpha are (A) -1,1, (B) 0,1 (C) 1,2, (D) -1,-1

8. 1+sin^(2)alpha=3sin alpha cos alpha ,then values of cot alpha are (A) -1,1, (B) 0,1 (C) 1,2, (D) -1,-1

The number of points from where a pair of perpendiculartangents can be drawn to the hyperbola, x^2 sec^2 alpha -y^2 cosec^2 alpha=1, alpha in (0, pi/4) , is (A) 0 (B) 1 (C) 2 (D) infinite

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]