`If cos alpha = k cos beta , "show that", "tan" ( alpha+beta)/2 = ( 1-k)/(1+k)"cot" (alpha-beta)/2`

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

If cot alpha cot beta=2 , show that (cos (alpha+beta))/(cos (alpha-beta))=(1)/(3)

If tan beta = (n sin alpha cos alpha)/(1-n sin^(2) alpha), "show that", tan (alpha - beta) = (1 - n) tan alpha.

If cot alpha cot beta=2 , show that (cos (alpha+beta))/(cos (alpha-beta)) = 1/3 .

If" " n tan alpha = (n+1) tan beta " then show that", tan (alpha - beta) = (sin 2 beta)/(2n + 1 - cos2 beta).

If cot alpha cot beta=2 show that (cos(alpha+beta))/(cos(alpha-beta))=1/3

If " "2 cos (alpha + beta) cos (alpha-beta)=1, "show that," tan^(2) alpha = (1-tan^(2) beta)/(1+3 tan^(2) beta)

If sin alpha sin beta - cos alpha cos beta + 1 = 0,"show that", sin (alpha + beta) = 0, "hence deduce that," 1 + cot alpha tan beta = 0.

If tan alpha=x+1,tan beta=x-1, show that 2cot(alpha-beta)=x^(2)