Let `-pi/6 < theta < -pi/12`. Suppose `alpha_1 and beta_1`, are the roots of the equation `x^2-2xsectheta + 1=0` and `alpha_2 and beta_2` are the roots of the equation `x^2 + 2xtantheta-1=0`. If `alpha_1 > beta_1` and `alpha_2 >beta_2`, then `alpha_1 + beta_2` equals:

Factorise alpha^2 +beta^2 + alpha beta

If cot (alpha + beta) = 0 , then sin (alpha + 2 beta) is equal to

If sin alpha+sin beta=a and cos alpha-cos beta=b then tan((alpha-beta)/2) is equal to-

Let log_3^N = alpha_1 + beta_1 , log_5^N = alpha_2 + beta_2 , log_7^N = alpha_3 + beta_3 Largest integral value of N if alpha_1 =5 , alpha_2 = 3 and alpha_3=2 and beta_1, beta_2, beta_3=(0,1) (A)342. (D) 242 (C) 243 (B) 343 342 17 Difference of largest and smallest integral values of N if alpha_1 =5 , alpha_2 = 3 and alpha_3=2 and beta_1, beta_2, beta_3=(0,1) (D) 99 (C) 98 (B) 100 (A) 97

If alpha = cos^(-1)((3)/(5)), beta = tan ^(-1)((1)/(3)) , where 0 lt alpha, beta lt (pi)/(2) , then alpha - beta is equal to

If Delta = |(cos (alpha_(1) - beta_(1)),cos (alpha_(1) - beta_(2)),cos (alpha_(1) - beta_(3))),(cos (alpha_(2) - beta_(1)),cos (alpha_(2) - beta_(2)),cos (alpha_(2) - beta_(3))),(cos (alpha_(3) - beta_(1)),cos (alpha_(3) - beta_(2)),cos (alpha_(3) - beta_(3)))|" then " Delta equals

If the roots of a_1x^(2)+b_1x+c_1=0 and alpha_1 , beta_1 and those of a_2x^(2)+b_2x+c_2=0 are alpha_2 , beta_2 such that alpha_1alpha_2=beta_1beta_2=1 then :

If alpha+beta=pi/4 then (1+tan alpha)(1+tan beta)=

If tan alpha =m/(m+1) and tan beta =1/(2m+1) , then alpha+beta is equal to

If sec alpha is the average of sec(alpha - 2beta) and sec(alpha + 2beta) then the value of (2 sin^2 beta - sin^2 alpha ) where beta!= n pi is