`2×2×2` is equal to?

If length of the perpendicular from the origin upon the tangent drawn to the curve x^2 - xy + y^2 + alpha (x-2)=4 at (2, 2) is equal to 2 then alpha equals

The value of |-1 2 1 3+2sqrt(2) 2+2sqrt(2) 1 3-2sqrt(2) 2-2sqrt(2) 1| is equal to a. zero b. -16sqrt(2) c. -8sqrt(2) d. none of these

If sintheta_1sintheta_2-costheta_1costheta_2+1=0, then the value of tan((theta_1)/2)cot((theta_2)/2) is equal to (a) -1 (b) 1 (c) 2 (d) -2

If sintheta_1sintheta_2-costheta_1costheta_2+1=0, then the value of tan((theta_1)/2)cot((theta_2)/2) is equal to -1 (b) 1 (c) 2 (d) -2

Prove that area common to ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and its auxiliary circle x^2+y^2=a^2 is equal to the area of another ellipse of semi-axis a and a-b.

In the ambiguous case, if a, b and A are given and c_1, c_2 are the two values of the third (c_1-c_2)^2 + (c_1+c_2)^2 tan^2 A is equal to

int_(-1)^(0) (dx)/( x^(2) + 2x+ 2) is equal to

In a DeltaABC ,a cos^(2)(B/2)+bcos^(2)(A/2) is equal to

{x inR:cos2x+2cos^(2)x=2} is equal to

If R denotes circumradius, then in DeltaABC,(b^2-c^2)/(2aR) is equal to