If `z=1+i tan alpha where pi lt alpha lt(3pi)/(2),` then what is `|z|` equal to ?

If sin alpha = (-3)/(5), where pi lt alpha lt (3pi)/(2), then cos ((alpha)/(2))=

If z=1+i tan alpha where pi

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 (1+tan alpha)(1+tan4 alpha)=2 where alpha in(0,(pi)/(16)) then alpha equal to

If 0 lt alpha lt (pi)/(6) then alpha(cosec alpha) is

If tan alpha =2 and 0 lt alpha lt (pi)/(2) then prove that x =a, pi +alpha are the solution of the equation (tan(2alpha-x))/(tan (2alpha+x))=11 that lies between 0 and 2pi

if (1+tan alpha )(1+tan4 alpha ) =2 where alpha in (0 , pi/16 ) then alpha equal to

If sin alpha = 3/5 , where (pi)/2 lt alpha lt pi , evaluate cos 3 alpha .

If |z-i|=1 and arg (z) =theta where 0 lt theta lt pi/2 , then cottheta-2/z equals