If `sintheta=nsin(theta+2alpha)` then prove that, `tan(theta+alpha)=(1+n)/(1-n)tanalpha`

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

if tanbeta=(nsinalphacosbeta)/(1-nsin^2alpha) then prove that tan(alpha-beta)=(1-n)tanalpha.

If costheta=(cosalphacosbeta)/(1-sinalphasinbeta) then prove that tan((theta)/(2))=(tan((alpha)/(2))-tan((beta)/(2)))/(1-tan((alpha)/(2))tan((beta)/(2)))

If sin(theta+alpha)=aandsin(theta+beta)=b , then prove that cos2(alpha-beta)-4abcos(alpha-beta)=1-2a^(2)-2b^(2) .

If sintheta + sin^(2)theta = 1 , prove that cos^(2)theta + cos^(4)theta = 1

If 3 cos theta+4 sin theta=A sin (theta+alpha) , then values of A and alpha are

A particle thrown over a triangle from one end of a horizontal base falls on the other end of the base after grazing the vertex. If alpha and beta are the base angles of triangle and angle of projection is theta , then prove that ( tan theta = tan alpha + tan beta)

If cosec theta + cot theta =k , then prove that cos theta =(k^(2)-1)/( k^(2)+1)

If A=[{:(costheta,sintheta),(-sintheta,costheta):}] then prove that A^(n)=[{:(cosntheta,sinntheta),(-sinn theta,cosntheta):}],n inN .

If acos2theta+bsin2theta=c has alphaandbeta as its roots, then prove that tanalpha+tanbeta=(2b)/(a+c) .