`Statement I : If `a, b in [0, p] then `sin(alpha+beta)/2<(sinalpha+sinbeta)/2` Statement II : If `3 cosx = 2 cos(x-2y)` then `tan(x-y) tany=5`

If tan alpha and tan beta are the roots of x^(2) + ax + b = 0, then (sin (alpha + beta))/(sin alpha sin beta) is equal to

If tan alpha and tan beta are the roots of x^2 + ax +b =0 then (sin(alpha+beta))/(sin alpha sin beta) is equal to

If sin(alpha+beta)=1 and sin(alpha-beta)=1/2 where alpha,beta in [0,pi/2] , then tan(2alpha+beta)=

Statement I : If m cos(theta+alpha)=n cos (theta-alpha) then tan theta.tan alpha=(m+n)/(m-n) Statement II : If (sin(alpha+beta))/(sin(alpha-beta))=(a+b)/(a-b) then tan alpha.cot beta=(a)/(b) Which of the above statements is correct ?

If tan alpha and tan beta are the roots of x^(2)+ax+b=0 then (sin (alpha+beta))/(sin alpha sin beta) is equal to ........... .

csc^(2)(alpha+beta)-sin^(2)(beta-alpha)+sin^(2)(2 alpha-beta)=cos^(2)(alpha-beta) where alpha,beta in(0,(pi)/(2)), then sin(alpha-beta) is equals

Statement-I : If f(theta)=(cot theta)/(1+cot theta) and alpha+ beta=(5pi)/(4) then f(alpha) f(beta)=(1)/(2) Statement-II : If alpha+ beta=(pi)/(2) and beta+ gamma= alpha then tan alpha= tan beta+ 2tan gamm Statement-III sin^(2) alpha+ cos^(2) (alpha+ beta)+2 sin alpha beta cos (alpha+beta) is independent of alpha only

If cos(theta - alpha)=a, cos(theta-beta)=b , then sin^(2)(alpha -beta) + 2abcos(alpha-beta)=0

If cos(alpha+beta)=0 then sin^(2)alpha+sin^(2)beta