If `t a nalpha=p/q` , where `alpha=6beta,alpha` being acute angle, prove that `1/2{pcos e c2beta=qsec2beta}=sqrt(p^2+q^2)`

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

If sin (alpha + beta) = 4/5 , sin (alpha -beta) = (5)/(13), alpha + beta , alpha - beta being acute angles prove that tan 2 alpha = (63)/(16).

Let tanalpha = a/b, alpha being an acute angle. Denote by f(a,b) the value of the expression a " cosec "2beta - b sec 2beta, where alpha = 6 beta . Then f(8,15) is equal to …………….

If cos^2alpha-sin^2alpha=tan^2beta," then prove that "tan^2alpha=cos^2beta-sin^2beta .

alpha and beta are acute angles and cos2alpha = (3cos2beta-1)/(3-cos2beta) then tan alpha cot beta =

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

If sin(alpha+beta)=1 and sin(alpha-beta)=1/2 , where 0lt=alpha, betalt= pi/2 , then find the values of tan(alpha+2beta) and tan(2alpha+beta) .

if abs({:(sinalpha, cosbeta), (cosalpha, sinbeta):})=1/2 , where alpha, beta are acute angles, then find the value of alpha+beta . a) pi/3 b) (2pi)/3 c) pi/2 d) pi/4

Prove that : cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+beta)=sin^2beta

If alphaa n dbeta are acute angles satisfying cos2alpha=(3cos2beta-1)/(3-cos2beta),t h e ntanalpha= sqrt(2)tanbeta (b) 1/(sqrt(2))t a nbeta (c) sqrt(2)cotbeta (d) 1/(sqrt(2))cotbeta