If `cosalpha+secalpha=2`, show that `cos^3alpha+sec^3alpha=2`.

If 3cos alpha-4sinalpha=5 , show that, 3sinalpha+4cosalpha=0 .

If cos^2alpha=sin^3alpha then show that tan^6alpha-tan^2alpha=1

If cosec alpha+cot alpha=2+sqrt(5) , show that, cosalpha=2/sqrt(5) .

if tan theta=(sinalpha-cosalpha)/(sinalpha+cosalpha) show that, sin alpha+cosalpha=pmsqrt(2)cos theta

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

If 2sec^2 alpha- sec^4 alpha-2 cosec^2 alpha+cosec^4 alpha=15/4 then tan alpha=

If cos (beta - gamma) + cos (gamma - alpha) + cos (alpha - beta) = -3/2, "show that", cos alpha + cos beta + cos gamma = 0 "and" sin alpha + sin beta + singamma = 0."Hence deduce that," cos (beta - gamma) = cos (gamma - alpha) = cos (alpha - beta) = -1/2.

If cos^2theta-sin^2 theta = tan^2 alpha , then show that cos^2 alpha -sin^2 alpha = tan^2 theta .

cos(beta-gamma)+cos(gamma-alpha)+cos(alpha-beta)=-3/2 show that cosalpha+cosbeta+cosgamma=0 and sinalpha+sinbeta+singamma=0 also cos(beta-gamma)=cos(gamma-alpha)=cos(alpha-beta)=-1/2 .

If " "cos(alpha - beta) + 1 = 0," show that ", cosalpha + cos beta = 0 " and " sin alpha + sin beta = 0.