If `m sin (alpha+beta)=cos(alpha-beta)`, prove that `1/(1-m sin 2alpha)+ 1/(1-msin2beta)=2/(1-m^2)`

If m sin (alpha+beta) = cos (alpha-beta) , prove that (1)/(1- m sin 2 alpha)+(1)/(1-m sin 2 beta)=(2)/(1-m^(2)) .

If sin alpha sin beta-cos alpha cos beta+1=0, then prove that 1+cot alpha tan beta=0

(sinalpha cos beta+cos alpha sin beta)^2+(cos alpha cos beta-sin alpha sin beta)^2=1

If sin alpha sin beta-cos alpha cos beta+1=0 , then prove that 1+cotalpha tan beta=0 .

If sin alpha+sin beta=a and cos alpha+cos beta=b prove that :cos(alpha-beta)=(1)/(2)(a^(2)+b^(2)-2)

If tan(alpha+beta)=n tan(alpha-beta) then show that (n+1)sin2 beta=(n-1)sin2 alpha

If sin alpha+sin beta=a and cos alpha+cos beta=b show that sin(alpha+beta)=(2ab)/(alpha^(2)+beta^(2))

If sin (alpha + beta)=1, sin (alpha- beta)= (1)/(2) , then tan (alpha + 2beta) tan (2alpha + beta) =

If sin(alpha+beta)=1,sin(alpha-beta)=(1)/(2) then tan(alpha+2 beta)tan(2 alpha+beta)=

if tan beta=(n sin alpha cos beta)/(1-n sin^(2)alpha) then prove that tan(alpha-beta)=(1-n)tan alpha