Prove that `2tanbeta+cotbeta=tanalphaimplies2tan(alpha-beta)=cotbeta`.

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 3 sin alpha=5 sin beta , then (tan((alpha+beta)/2))/(tan ((alpha-beta)/2))=

A jet plane is at a vertical height of h. The angles of depression of two tanks on the ground in the same line with the plane are alpha and beta (alpha gt beta) . Prove that the distance between the tanks is ( h (tan alpha - tan beta))/(tan alpha tan beta)

prove that : tan(alpha)+2 tan(2alpha) +4(tan4alpha)+8cot(8alpha) = cot(alpha)

A window of a house is h metres above the ground. From the window, the angles of elevation and depression of the top and the bottom of another house situated on the opposite sides of the lane are found to be alpha and beta respectively. Prove that the height of the other house is h(1 + tan alpha cot beta) metres.

Prove that, tan3A.tan2A.tanA=tan3A-tan2A-tanA

If alpha+beta+gamma=2pi , then show that tan.alpha/2 + tan.beta/2 + tan.gamma/2 = tan.alpha/2 tan.beta/2 tan.gamma/2 .

A building stands on a horizontal plane and is surmounted by a vertical flag-stagg of height h. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are alpha and beta respectively. Prove that the height of the building is (h tan alpha)/(tan beta-tan alpha)

Show that the lines (1-cos theta tan alpha) y^2 -(2cos theta+sin ^2 theta tan alpha )xy +cos theta (cos theta+tan alpha )x^2=0 include an angle alpha between them .

Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),((gamma+alpha-beta-delta)^4,(gamma+alpha-beta-delta)^2,1),((alpha+beta-gamma-delta)^4,(alpha+beta-gamma-delta)^2,1)|=-64(alpha-beta)(alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta)(gamma-delta)