If `tan^(- 1)(1/2) + tan^(- 1)2=alpha `,then prove that ` alpha=9 0^(@)`

If tan^(-1)((1)/(2))+tan^(-1)2=alpha, then prove that alpha=90^(@)

If tan^2alpha = 1 + tan^2beta ,then prove that cos^2 beta = cot^2alpha

If sin alpha = lamda sin (theta - alpha ) then prove that tan (alpha - (theta)/(2)) = (lamda -1)/( lamda +1) tan ""(theta)/(2).

if tan beta=(n sin alpha cos beta)/(1-n sin^(2)alpha) then prove that tan(alpha-beta)=(1-n)tan alpha

if tan beta=(n sin alpha cos beta)/(1-n sin^(2)alpha) then prove that tan(alpha-beta)=(1-n)tan alpha

If 2tan^(2)alpha tan^(2)beta tan^(2)gamma+tan^(2)alpha tan^(2)beta+tan^(2)beta tan^(2)gamma+tan^(2)gamma tan^(2)alpha=1 prove that sin^(2)alpha+sin^(2)beta+sin^(2)gamma=1

If u=cot^(-1)sqrtcos alpha-tan^(-1)sqrt(cosalpha) then prove that sincup=tan^2(alpha/2) .

If tan^(2)alpha=1+2tan^(2)beta, prove that,cos2 beta=1+2cos2 alpha

If 2 tan^2 alpha tan^2 beta tan^2 gamma+ tan^2 alpha tan^2 beta+ tan^2 beta tan^2 gamma+ tan^2 gamma tan^2 alpha=1 , prove that sin^2 alpha+ sin^2 beta+ sin^2 gamma =1 .

If -(pi)/2 lt alpha lt (pi)/2 then prove that tan^(-1)((3sin 2 alpha)/(5+3 cos alpha))+tan^(-1)((tan alpha)/4)=