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

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

If tan alpha+cotalpha=2, show that, tan^7alpha+cot^7alpha=2.

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

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

If (tan (alpha- beta+ gamma))/(tan (alpha+ beta- gamma))=(tan beta)/( tan gamma) , show that either sin (beta- gamma)=0 or sin 2 alpha+ sin 2 beta+ sin 2 gamma=0

If alpha,beta,gamma are three real numbers and A=[(1,"cos"(alpha-beta),"cos"(alpha-gamma)),(cos(beta-alpha),1,"cos"(beta-gamma)),("cos"(gamma-alpha),"cos"(gamma-beta),1)] , then which of following is/are true? a. A is singular b. A is symmetric c. A is orthogonal d. A is not invertible

If (cosalpha+cosbeta+cosgamma)=0, sinalpha+sinbeta+singamma=0 then show that cos3alpha+cos3beta+cos3gamma=3cos(alpha+beta+gamma)