using cotA-tanA=2cot2A deduce that `tanalpha+tan2 alpha+4tan4alpha+8cot8alpha=cotalpha`

cot^(-1)(sqrtcosalpha)-tan^(-1)(sqrt(cos alpha))=x , then sin x is equal to a) tan^2""alpha/2 b) cot^2""alpha/2 c) tan alpha d) cot ""alpha/2

If u = cot^(-1)sqrt(tan alpha ) - tan ^(-1)sqrt(tan alpha) then tan (pi/4-u/2) is a) sqrt(tan alpha) b) sqrt(cot alpha) c) tan alpha d) cot alpha

Derive the following relation: alpha_a=2alpha_l

If A=[(cos^2alpha,cosalphasinalpha),(cosalphasinalpha,sin^2alpha)] and B=[(cos^2beta,cosbetasinbeta),(cosbetasinbeta,sin^2beta)] . Show that AB=[(cosalphacosbetacos(alpha-beta),sinbetacosalphacos(alpha-beta)),(cosbetasinalphacos(alpha-beta),sinbetasinalphacos(alpha-beta))]

If sin theta = 3 sin (theta + 2 alpha) , then the value of tan (theta + alpha) + 2 tan alpha is

If sin theta=n sin (theta+2a) ,show that tan(theta+alpha)=(1+n)/(1-n) tan alpha .

If alphaandbeta are the two different roots of equation a costheta+bsintheta=c prove that (i) tan(alpha+beta)=(2ab)/(a^(2)-b^(2)) (ii) cos(alpha+beta)=(a^(2)-b^(2))/(a^(2)+b^(2))