`lim_(x->0)(sin(alpha+beta)x+sin(alpha-beta)x+sin2alpha x)/(cos^2betax-cos^2alphax)`

lim_(xto0) (sin(alpha+beta)x+sin(alpha-beta)x+sin2alphax)/(cos2betax-cos2alphax).x

lim_(xto0) (sin(alpha+beta)x+sin(alpha-beta)x+sin2alphax)/(cos2betax-cos2alphax).x

lim_(x rarr0)(sin(alpha+beta)x+sin(alpha-beta)x+sin2 alpha x)/(cos^(2)beta x-cos^(2)alpha x)

If tan alpha and tan beta are the roots of the equation x^(2) +px + q = 0 , then the value of sin^(2) (alpha +beta) + p cos (alpha + beta) sin (alpha + beta) + q cos^(2) (alpha + beta) is

2sin^(2)beta+4cos(alpha+beta)sin alpha sin beta+cos2(alpha+beta)=

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

tan alpha and tan beta are roots of the equation x^(2)+ax+b=0, then the value of sin^(2)(alpha+beta)+a sin(alpha+beta)*cos(alpha+beta)+b cos^(2)(alpha+beta) is equal to