If`sinalphasinbeta-cosalphacosbeta+1=0`then prove `cotalpha tanbeta=-1`

If costheta=(cosalpha-cosbeta)/(1-cosalphacosbeta) , then the values of tan(theta/2) is

If alpha,beta,gamma, in (0,pi/2) , then prove that (s i(alpha+beta+gamma))/(sinalpha+sinbeta+singamma)<1

If tanalpha=1/7 and tanbeta=1/3 , then cos 2alpha=

If tanalpha=1/5 , tanbeta=1/239 , then the value of tan(4alpha-beta) is

prove that cos^2theta(1 + tan^2 theta) = 1

prove that If tan theta + (1)/ (tan theta) = 2 then show that prove tan^2 theta + (1) / (tan^2 theta)

Prove that (sin theta - cos theta +1)/(sin theta + cos theta -1) = (1)/((sec theta - tan theta)).

If x, y, z are positive then prove that tan^-1(frac{x-y}{1+xy})+tan^-1(frac{y-z}{1+yz})+tan^-1(frac{z-x}{1+zx}) = 0

Prove the following: (frac(1+cottheta+cosectheta)(1-cottheta-cosectheta))=(frac(cosectheta+cottheta-1)(cottheta-cosectheta+1))

Prove that (frac(1+sintheta)(1+costheta)) + (frac(1-sintheta)(1-costheta)) = 2(cosec^2theta-cottheta)