If `at a nalpha+bt a nbeta=(a+b)tan((alpha+beta)/2)` , where `alpha!=beta` , prove that `acosbeta=bcosalphadot`

If a tan alpha+b tan beta=(a+b)tan((alpha+beta)/(2)) where alpha!=beta ,prove that a cos beta=b cos alpha

If a tan alpha+b tan beta=(a+b) tan ((alpha+beta)/2) , where alpha ne beta , prove that : a cos beta= b cos alpha .

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

If sin(alpha+beta)=1 and sin(alpha-beta)=1/2 where alpha,beta in [0,pi/2] , then tan(2alpha+beta)=

If alpha ne beta " and " a tan alpha + b tan beta = (a + b) "tan" (alpha + beta)/2,"show that" (cos alpha)/(cos beta) = a/b.

If cos alpha=tan beta and cos beta=tan alpha where alpha and beta are acute angles then sin alpha

If 2\ t a nalpha=3t a nbeta, prove that tan(alpha-beta)=(sin2beta)/(5-cos2beta)

If tan (alpha- beta )= (7)/(24) and tan alpha =(4)/(3) , where alpha and beta are in the first quadrant prove that alpha + beta = pi //2

If 2tan beta+cot beta=tan alpha, prove that cot beta=2tan(alpha-beta)

If tan alpha=(1-cos beta)/(sin beta), then a )tan3 alpha=tan2 beta(b)tan2 alpha=tan beta(c)tan2 beta=tan alpha(d) none of these