`If sin (alpha + beta) = n sin (alpha - beta) " and " n ne -1," prove that " cot alpha = (n-1)/(n+1) cot beta.`

If cot (alpha + beta )=0 , then sin(alpha+2beta ) =

If (sin beta)/(sin(2 alpha+ beta))=m/n , prove that : cot (alpha+ beta)= (n-m)/(n+m) cot alpha .

If tan alpha= n tan beta and sin alpha= m sin beta , prove that cos^2 alpha= (m^2-1)/(n^2-1) .

"If" (sin (alpha - beta))/(sin beta) = (sin (alpha + theta))/sin theta, " prove that " cot beta - cot theta = cot(alpha + theta) + cot (alpha - beta)

If tan alpha - tan beta =m and cot alpha - cot beta =n , then prove that cot ( alpha - beta )= (1)/(m)- (1)/(n)

If "tan" alpha= n tan beta and sin alpha =m sin beta prove that : cos^(2)alpha=(m^(2)-1)/(n^(2)-1)

If cos (alpha+beta) sin (gamma+delta)=cos (alpha-beta) sin (gamma-delta) , prove that : cot alpha cot beta cot gamma= cot delta .

If sin alpha sin beta-cos alpha cos beta+1=0, then prove that 1+cot alpha tan beta=0

If sin(theta+alpha)=n sin(theta-alpha) , prove that cot theta=(n-1)/(n+1) cot alpha .

If sin alpha sin beta - cos alpha cos beta + 1=0, then the value of 1+cot alpha tan beta is