By geometrical interpretation, prove that
`tan(alpha+beta)=(tanalpha+tanbeta)/(1-tanalphatanbeta)`.

(1+tanalphatanbeta)^2+(tanalpha-tanbeta)^2=

By geometrical interpretation, prove that (i) sin(alpha+beta)=sin alpha cos beta+sinbeta cosalpha (ii) cos(alpha+beta)=cosalpha cosbeta -sin alpha sinbeta

Prove that (tan alpha+tan beta)/(cot alpha+cot beta)=tan alpha tan beta

Prove that cos(alpha-beta)/(cos alpha sin beta)=tan alpha+cot beta

If cos theta=(cos alpha-cos beta)/(1-sin alpha sin beta), prove that one value of tan(theta)/(2)=(tan(alpha)/(2)-tan(beta)/(2))/(1-tan(alpha)/(2)-tan(beta)/(2))

An aeroplane is flying above a horizontal plane. The angle of depression of two consecutive mile stones at plane in opposite directions are respectively alpha and beta . Prove that height of the aeroplane is (tanalphatanbeta)/(tanalpha+tanbeta)

If tan beta=3tan alpha, prove that tan(alpha+beta)=(2sin2 beta)/(1+cos2 beta)

If 2tan alpha=3tan beta, prove that tan(alpha-beta)=(sin2 beta)/(5-cos2 beta)

If 2tan alpha=3tan beta, prove that tan(alpha-beta)=(sin2 beta)/(5-cos2 beta)

If alpha+beta=pi/4 then (1+tan alpha)(1+tan beta)=