`"If" (cot(alpha -beta))/(cot alpha) + (cos^(2) gamma)/(cos^(2) alpha) = 1," show that, " tan^(2) gamma + tan alpha cot beta = 0.`

If (cot(alpha-beta))/cotalpha+(cos^2gamma)/(cos^2alpha)=1 show that tan^2gamma+tanalphacotbeta=0

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

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

If cos beta cos (gamma- alpha)= cos (alpha- beta+ gamma) , prove that cot alpha+ cot y= 2cot beta

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

If cos alpha, sin alpha and cot alpha are in G.P. show that tan^(6)alpha- tan^(2)alpha=1

If |{:(1,cos alpha, cos beta),(cos alpha, 1 , cos gamma ),(cos beta, cos gamma , 1):}|=|{:(0,cos alpha, cos beta),(cos alpha , 0 , cos gamma),(cos beta, cos gamma, 0):}| then the value of cos^2 alpha + cos^2 beta + cos^2 gamma is : (a) 1 (b) 1/2 (c) 3/8 (d) 9/4

show that (1-sin^2 alpha)(1-cos^2 alpha)(1+cot^2 alpha)(1+tan^2 alpha) = 1.

If sin^(2) theta=(cos 2 alpha cos 2 beta)/(cos^(2)(alpha+ beta)) then, show that one value of "tan"^(2) (theta)/(2) " is " "tan" ((pi)/(4)-alpha) "tan" ((pi)/(4)+beta) .