[ 9.If 2tan^(-4)(cos theta)=tan^(-1)(2coscc theta), then show that theta=(pi)/(4) where n is any integer.]

If 2 tan^(-1)(costheta) = tan^(-1)(2 cosec theta) , then show that theta = (pi)/(4) , when n is an y integer.

If 2 tan^(-1)(costheta) = tan^(-1)(2 cosec theta) , then show that theta = (pi)/(4) , when n is an y integer.

If: tan (pi cos""theta/2)=cot(pisin"theta/2), then show that theta=sin^1(3/4).

(i) If sin(pi/2costheta) = cos(pi/2 sin theta) , show that, +- cos(theta + pi/4) =(4n+1)/sqrt(2) where n= any integer. (ii) If tan(pi cos theta) = cot(pi sin theta) , prove that, cos(theta - pi/4) = (2n+1)/(2sqrt(2)), n=0, -1,1,-2,2 ,............

If tan((pi)/(4)+theta)+tan((pi)/(4)-theta)=4 then theta=

If tan (pi cos theta)= cot (pi sin theta) , show that cos (theta-(pi)/(4))=+- (1)/(2sqrt(2))

If tan (pi//4 + theta) + tan (pi//4 - theta) = 4 , then theta =

If tan^4theta - tan^2 theta= 1 , then prove that cos^4theta+ cos^2theta = 1

If tan (pi cot theta )= cot (pi tan theta) , then show that tan theta= (1)/(4)[ 2 n+ 1+- sqrt(4n^(2)+4n-15)] , where n gt 1 or n lt -2 .