`If cos theta = n cos ( theta + 2 phi) "show that"(n+1) tan ( theta + phi)= (n-1) cot phi`

If sin theta = k sin (theta + phi),"show that", tan(theta + phi) = (sin phi)/(cos phi -k).

If cot theta = cos (x+y) "and" cot phi = cos (x-y), "show that" tan (theta- phi)=(2sin x sin y )/(cos^(2) x + cos^(2) y)

If 2 tan theta = cot phi, "show that" cos(theta - phi) = 3 cos ( theta + phi).

If " "a cos phi = b cos theta," show that " a tan theta + b tan phi = (a+b) tan ((theta + phi)/2)

sintheta=ksin(theta+phi) .show that tan(theta+phi)=(sinphi)/(cosphi-K)

"If" (n tan theta)/(cos^(2) (alpha - theta))= (m tan (alpha - theta))/(cos^(2) theta) "then show that" tan ( alpha - 2 theta) = (n-m)/(n+m) tan alpha

If tan theta = cos2 alpha tan phi, prove that tan (phi - theta) = (tan^(2) alpha sin 2 phi)/(1+ tan^(2) alpha cos 2 phi)

If sin theta + sin phi = a, cos theta + cos phi = b prove that tan ((theta-phi)/2 )=pm sqrt((4-a^(2)-b^(2))/(a^(2)+b^(2)))

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 .

(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 ,............