`(sin theta)/(cos3theta)+(sin3theta)/(cos9theta)+(sin9theta)/(cos27theta)+(sin27theta)/(cos81theta)=`

(sin theta)/(cos(3theta))+(sin(3theta))/(cos(9theta))+(sin(9theta))/(cos(27theta))+(sin(27theta))/(cos(81theta))=

Prove that : sintheta/cos(3theta)+sin(3theta)/cos(9theta)+sin(9theta)/cos(27theta)=1/2(tan(27theta)-tan(theta))

If A= tan27theta - tantheta and B= (sintheta)/(cos 3theta) +(sin 3theta)/(cos 9theta) + (sin 9theta)/(cos 27theta) , then the value of (A+B)/(A-B) +(A-B)/(A+B) -10/3 is

If k_1=tan 27 theta-tan theta and k_2=(sintheta)/(cos3theta)+(sin3theta)/(cos9theta)+(sin9theta)/(cos27theta) then,

Prove that (cos^3 theta-sin^3 theta)/(cos theta-sin theta) = 1+cos theta sin theta

Prove that: (sin2theta)/(costheta cos3theta)+(sin4theta)/(cos3theta.cos5theta)+(sin6theta)/(cos5theta.cos7theta)+… to terms = 1/(2sintheta) [sec(2n+1)theta-sectheta]

Prove that (cos^3theta+sin^3 theta)/(cos theta+sin theta)+(cos^3 theta-sin^3 theta)/(cos theta-sin theta)=2

If the system of linear equations {:((cos theta)x + (sin theta) y + cos theta=0),((sin theta)x+(cos theta)y + sin theta=0),((cos theta)x + (sin theta)y -cos theta=0):} is consistent , then the number of possible values of theta, theta in [0,2pi] is :

Prove that: (a) (sin 2 theta)/(1+cos 2 theta)=tan theta (b) (1+sin 2 theta+cos 2theta)/(1+sin2 theta-cos 2 theta)=cot theta

(2 sin theta*cos theta - cos theta)/(1-sin theta+sin^2 theta-cos^2 theta) = cot theta