if `tanalpha -tanbeta =x` and `cotbeta-cotalpha =y` prove that `cot(alpha-beta) = (x+y)/(xy)`

If 2tanbeta+cotbeta=tanalpha , prove that cotbeta=2tan(alpha-beta)dot

If alpha+beta=theta and (tan alpha)/(tan beta) = x/y , prove that sin (alpha-beta) = (x-y)/(x+y) sin theta

If tan - A tan B = x, cot B - cot A = y prove that cot (A - B) = (1)/(x) + (1)/(y)

If alpha + beta = 90^@ and beta + gamma = alpha then tanalpha-tanbeta=?

1/(tan3alpha-tanalpha)-1/(cot3alpha-cotalpha)=cot2alpha

If t a nalpha=x+1,tanbeta=x-1, show that 2cot(alpha-beta)=x^2dot

(i) If tanA-tan B=x and cot B- cot A=y . Prove that cot(A-B)=1/x + 1/y . (ii) If 2 cos A = x+1/x, 2 cos B = y + 1/y , then show that 2 cos (A-B)= x/y+y/x .

If acos2theta+bsin2theta=c has alpha and beta as its roots, then prove that tanalpha+tanbeta=(2b)/(a+c) .

If 2|sin2alpha|=|tanbeta+cotbeta|,alpha,beta in (pi/2,pi), then the value of alpha+beta is (a) (3pi)/4 (b) pi (c) (3pi)/2 (d) (5pi)/4

If acos2theta+bsin2theta= c, alpha and beta as its roots , then prove that tanalpha+t a nbeta=(2 b)/(a+c) , tanalpha*t a nbeta=(c-a)/(c+a) , tan(alpha+beta)=b/a