If `tanx tany=a` and `x+y=2b` show that `tanx and tany` are the roots of the equation `z^2-(1-a)tan2b*z+a=0`

Solve the equation, (1-tanx)(1+sin2x)=1+tanx

If tanx=2/3 and tany=3/4 then tan(x+y)=

If a, b, c are non - zero real numbers, the system of equations y+z=a+2x, x+z=b+2y, x+y=c+2z is consistent and b=4a+(c )/(4) , then the sum of the roots of the equation at^(2)+bt+c=0 is

In a triangle ABC, A > B, if the measure of angleA and angleB satisfy the equation (2tanx)/(1+tan^2x)=lambda,0

Let f(x)=max{tanx, cotx} . Then the number of roots of the equation f(x)=(1)/(2)" in "(0, 2pi) is

Prove tanx+ tany+ tanz=tan xtany tanz if x+y+z = pi

If tanx=a/(a+1) and tany=1/(2a+1) then show that one of the values of x+y=pi/4; a in R, a!= -1, a!= -1/2

If (tanx - tany)^(2) ,(tany-tanz)^(2) and (tanz-tanx)^(2) are in A.P then tanx-tany, tany-tanz, tanz-tanx are in

If z_(1) and z_(2) are the roots of the equation az^(2)+bz+c=0,a,b,c in complex number and origin z_(1) and z_(2) form an equilateral triangle,then find the value of (b^(2))/(ac) .