A to Z Exams

A+B= C⇒cos2A +cos2B + cos2C - 2 cos A cos B cos C

If (tan 3A / tan A) =α then ( sin 3A/ sin A) =

If sin-1x+sin-1(1-x)=cos-1x, then x ε to

In a ∆ ABC, (a-b)2cos2(C/2)+(a+b)2sin2(C/2) is equal to

If  cos θ - 4 sin θ = 1 then  sin θ + 4 cos θ   is equal to

The expression tan 90– tan 270– tan 630is equal to :

In a ΔABC, cos[(B+2C+3A)/2]+cos[(A-B)/2] is equal to

The angle between the lines represented by y2sin2θ-xysin2θ+x2(cos2θ-1)=0 is

The number of natural numbers less than 1000, in which no two digits are repeated, is :

In ΔABC, 1+4 sin(π-A/4)sin(π-B/4)sin(π-C/4)=

Log3√2324 =

1- cos A+ cos B- cos (A+B)/1+cos A- cos B- cos(A+B)=

(sin θ+ cosec θ)2+(cos θ+ sec θ)2 =

If sin α+ sin β= a, cos α+ cos β = b then sin(α+β)=

In ΔABC , cos(A+2B+3C/2)+cos(A-C/2) =

If A+B+C= 2S, then cos2 S+ cos2 (S-A)+ cos2 (S-B)+ cos2 (S-C)=

If A+B+C=1800 then cos 3A+cos 3B+cos 3C=

The point on the line 3x+4y = 5 which is equidistant from (1,2) and (3,4) is

If X follows a binomial distribution with parameters n = 6 and p. If 4P(X = 4) = P(X = 2), then p is equal to

If log2(sin x)- log2(cos x)- log2(1-tan x)- log2(1+tan  x)= -1 then tan 2x=

In ΔABC,   tan (A/2)tan (B/2)+ tan (B/2)tan (C/2)+ tan (C/2) tan (A/2)=

If k=(1+sin A)(1+sinB)(1+sin C)=(1-sinA)(1-sin B)(1-sin C) then k=

P(-1, -3) is a centre of similitude for the two circles x2+y2=1 and x2+y2-2x-6y+6=0. The length of the common tangent through P to the circle is

If x cos α= y cos(2π/3+ α)= z cos(4π/3+ α),then xy+yz+zx=

If cos θ= 3/5 and θ is not in the first quadrant,then (5tan(π+ θ)+4 cos(π- θ))/(5sec(2π-θ)- 4 cot(2π+θ) )

The range of 5 Co-1(3x) is

The point (3, 2) undergoes the following three transformations in the order given i) Reflection about the line y = x ii) Translation by the distance 1 unit in the positive direction of x – axis iii) Rotation by an angle π/4 about the origin in the anticlockwise direction. Then the final position of the point is

(cos 2α /cos4α- sin4 α)- (cos4 α+ sin4 α/ 2- sin22α)=

Find the equation of the parabola, whose axis parallel to the y-axis and which passes through the points (0,4),(1,9) and (4,5) is

The value of (i)i is equal to