Prove that `|[a_1alpha_1+b_1beta_1, a_1alpha_2+b_1beta_2, a_1alpha_3+b_1beta_3], [a_2alpha_1+b_2beta_1, a_2alpha_2+b_2beta_2, a_2alpha_3+b_2beta_3], [a_3alpha_1+b_3beta_1, a_3alpha_2+b_3beta_2, a_3alpha_3+b_3beta_3]|=0`

Eliminte alpha and beta : a sin alpha=bsin beta, a cos^2alpha+bcos^2beta=1 ,a cot^2alpha+b cot ^2beta=1

If sin 2 alpha = 4 sin 2 beta, "show that", 5tan ( alpha -beta) = 3 tan ( alpha +beta)

tan (alpha + beta) =1/2, tan(alpha - beta) = 1/3 "then the value of" tan^(2) alpha is-

If the roots of equation x^3+a x^2+b=0a r ealpha_1,alpha_2 and alpha_3(a ,b!=0) , then find the equation whose roots are (alpha_1alpha_2+alpha_2alpha_3)/(alpha_1alpha_2alpha_3),(alpha_2alpha_3+alpha_3alpha_1)/(alpha_1alpha_2alpha_3),(alpha_1alpha_3+alpha_1alpha_2)/(alpha_1alpha_2alpha_3)

Prove that, |{:(alpha,beta,gamma),(alpha^2,beta^2,gamma^2),(beta+gamma,gamma+alpha,alpha+beta):}|=(alpha-beta)(beta-gamma)(gamma-alpha)(alpha+beta+gamma)

If |alpha|,|beta| lt 1, s _(1) =1- alpha +alpha^(2) -alpha^(3)+…oo and s_(2)=1-beta +beta ^(2) -beta ^(3)+…oo then (1-alpha beta +alpha^(2) beta ^(2) -alpha ^(3) beta ^(3) +…oo) is equal to

If tan theta = ( tan alpha + tan beta)/(1 + tan alpha tan beta),"show that " sin 2 theta =(sin 2 alpha + sin 2 beta)/(1+sin 2 alpha sin 2 beta)

If tan theta = ( tan alpha - tan beta)/(1-tan alpha tan beta),"show that", sin 2 theta=(sin 2 alpha- sin 2 beta)/(1- sin2 alpha sin 2 beta).

If cot alpha cot beta = 3,"show that", (cos (alpha - beta))/(cos (alpha + beta)) =2

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.