If `(cosx)/(cos(x-2y))=lamda`, then show that `tan(x-y)=((1-lamda)/(1+lamda))coty`.

If sin alpha = lamda sin (theta - alpha ) then prove that tan (alpha - (theta)/(2)) = (lamda -1)/( lamda +1) tan ""(theta)/(2).

Let f (x) = (cos ^(2) x)/(1+ cos x+cos ^(2)x )and g (x) =lamda tan x+(1-lamda) sin x-x, where lamda in R and x in [0, pi//2). The values of 'lamda' such that g '(x) ge 0 for any x in [0, pi//2):

The value of lamda or which the straighat line (x-lamda)/3=(y-1)/(2+lamda)=(z-3)/(-1) may lie on the plane x-2y=0 (A) 2 (B) 0 (C) -1/2 (D) there is no such lamda

The value of lamda for which the lines (x-1)/1=(y-2)/(lamda)=(z+1)/(-1) and (x+1)/(-lamda)=(y+1)/2=(z-2)/1 are perpendicular to each other is

Find the value of lamda so that the lines (1-x)/(3)=(7y-14)/(2lamda)=(z-3)/(2) and (7-7x)/(3lamda)=(y-5)/(1)=(6-z)/(5) are at right angles.

Find the value of lamda such that the line (x-1)/(2)=(y-1)/(3)=(z-1)/(lamda) is bot to normal to the plane vecr.(2veci+3vecj+4veck)=0 .

The number of distinct real values of lamda for which (x-1)/1=(y-2)/2=(z+3)/(lamda^(2)) and (x-3)/1=(y-2)/(lamda^(2))=(z-1)/2 are coplanar, is

If the lines (x-2)/(1)=(y-3)/(1)=(z-4)/(lamda) and (x-1)/(lamda)=(y-4)/(2)=(z-5)/(1) intersect then

Find the value of lamda so that the straight lines: (1-x)/(3)= (7y -14)/(2 lamda)= (z-3)/(2) and (7-7x)/(3 lamda)= (y-5)/(1)= (6-z)/(5) are at right angles.

If lamda_(1) is the product of values of x satisfy the equation (x)^(log_(3)x)=(x^(9))/((3)^(20)) and lamda_(2) is the number of integers in the solution set of the inequality log_(x)(4x-3)ge2 , the ((lamda_1)/2187+lamda_(2)) equals