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

Factorise alpha^2 +beta^2 + alpha beta

If cos alpha=4/5 and cos beta =5/13, prove that cos (alpha-beta)/2=28/65.

alpha + beta = 5 , alpha beta= 6 .find alpha - beta

If alpha and beta are acute such that alpha+beta and alpha-beta satisfy the equation tan^(2)theta-4tan theta+1=0 , then (alpha, beta ) =

If sin alpha=4/5 and cos beta =5/13, prove that cos ((alpha-beta)/2)=8/sqrt 65.

If 3 sin alpha=5 sin beta , then (tan((alpha+beta)/2))/(tan ((alpha-beta)/2))=

If (log)_(10)(1025)/(1024)=alpha and (log)_(10) 2=beta, then the value of (log)_(10)4100 in terms of alpha and beta is equal to a. alpha+9beta b. alpha+12beta c. 12alpha+beta d. 9alpha+beta

If (log)_(10)(1025)/(1024)=alphaa n d(log)_(10)=beta, then the value of (log)_(10)4100 in terms of alpha and beta is equal to a. alpha+9beta b. alpha+12beta c. 12alpha+beta d. 9alpha+beta

If alpha+beta= 60^0 , prove that cos^2 alpha + cos^2 beta - cosalpha cos beta = 3/4 .

If (log)_(10)(1025)/(1024)=alphaa n d(log)_(10)2=beta , then the value of (log)_(10)4100 in terms of alphaa n dbeta is equal to alpha+9beta (b) alpha+12beta 12alpha+beta (d) 9alpha+beta