If `log_12 18=alpha and log_24 54=beta`. Prove that `alpha beta+5(alpha-beta)=1`

If log_(12)18=alpha and log_(24)54=beta then the value of alpha beta+alpha-beta

Prove that |cos alpha-cos beta|<=| alpha-beta|

| alpha alpha1 beta F|=(alpha-P)(beta-alpha)

If cos alpha+cos beta=0=sin alpha+sin beta. Prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)

Given that (log)_p x=alpha\ a n d(log)_q x=beta,\ then value of equals- a. (alphabeta)/(beta-alpha) b. (beta-alpha)/(alphabeta) c. (alpha-beta)/(alphabeta) d. (alphabeta)/(alpha-beta)

If (log)_(10)(1028)/(1024)=alpha and(log)_(10)=beta, then the value of (log_(10))_(10)4100 in terms of alpha and beta is equal to a.alpha+9 beta b.alpha+12 beta c.12 alpha+beta d .9 alpha+beta

If cos alpha+cos beta=0=sin alpha+sin beta, then prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)

If cos alpha+cos beta=0=sin alpha+sin beta, then prove that cos2 alpha+cos2 beta=-2cos(alpha+beta)

If coa alpha+cos beta=(1)/(3) and sin alpha+sin beta prove that cos((alpha-beta)/(2))=+-(5)/(24)

If alpha,beta, are roots of the equation x^(2)+sqrt(x)alpha+beta=0,beta beta then values of alpha and beta are 1. alpha=1 and beta=12 .alpha=1 and beta=-2 3.alpha=2 and beta=1alpha=2 and beta=-2