If `alpha` and `beta` be two acute angles and `cos2alpha=(3cos2beta-1)/(3-cos2beta)`,show that `tan alpha=sqrt2tanbeta`

If tanbeta=(nsinalphacosalpha)/(1-nsin^2alpha) ,show that tan(alpha-beta)=(1-n)tanalpha

If alpha and beta are the solution of the equation a tan theta +b sec theta=c ,then show that tan(alpha+beta)=2ac/(a^2-c^2)

Find cot^2 alpha- cos^2 alpha . .

If cos^2alpha-sin^2alpha=tan^2beta ,show that cos^2beta-sin^2beta=tan^2alpha

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

If cos alpha=13/14 and cos beta=1/7 where alpha and beta are acute angles,show that alpha-beta=pi/3 .

If alpha+beta=gamma ,show that cos^2alpha+cos^2beta+cos^2gamma=1+2cosalphacosbetacosgamma

If tan alpha=m/(m+1) and tan beta=1/(2m+1) ,prove that alpha+beta=pi/4 .

If alpha and beta are roots of x^2 - 6x + a = 0 and 3alpha + 2beta = 20 , find the value of a.