If `mtan (theta-30^(@))=n tan (theta+120^(@))` show that `cos 2 theta=(m+n)/(2(m-n))`

if m*tan(theta-30)=n*tan(theta+120) , show that cos2theta=(m+n)/(2(m-n)) .

tan^(2) theta-sec^(2) theta=….

If tan theta = sqrt2-1 then tan (2theta)=1 .

Show that tan ^(2) theta +tan ^(4) theta =sec ^(4) theta -sec ^(2) theta

Show that (cosec theta -cot theta )^(2) =(1-cos theta )/( 1+cos theta )

If msintheta=nsin(theta+2alpha) , then prove that tan(theta+alpha)cotalpha=(m+n)/(m-n) .

If 0 lt theta lt (pi)/2 and 5 tan theta = 4 then (5 sin theta - 3 cos theta) / (sintheta +2 cos theta ) = 5/14

If tan^(4)theta +tan^(2) theta = 1 , then the value of cos^(4)theta +cos^(2)theta is-

Find (dy)/(dx) : x=2 cos theta- cos^(2) theta and y=2 sin theta- sin 2theta Show that (dy)/(dx)= -1 " when " theta = (pi)/(2)

Evaluate the following (sin theta +cos theta )^(2) +(sin theta -cos theta )^(2)