3K" Etan "alpha=(p)/(q)" where "alpha=6 beta,alpha" being an acute angle,prove that: "(1)/(2)(pcosec2 beta-q sec2 beta)=sqrt(p^(2)+9)

If tan(alpha)=(p)/(q) where alpha=6 beta,alpha being an acute angle,prove that: (1)/(2)(p cos ec2 beta-sec2 beta)=sqrt(p^(2)+q^(2))

If tan alpha=(p)/(q), where alpha=6 beta,alpha being acute angle,prove that (1)/(2){p cos ec2 beta-q sec2 beta}=sqrt(p^(2)+q^(2))

If tan alpha= p/q , where alpha=6 beta, alpha being an acute angle, prove that : 1/2 {p cosec 2 beta- qsec 2 beta} = sqrt(p^2 +q^2) .

If t a nalpha=p/q , where alpha=6beta,alpha being acute angle, prove that 1/2{pcos e c2beta-qsec2beta}=sqrt(p^2+q^2)

If sin (alpha + beta) = 4/5 , sin (alpha -beta) = (5)/(13), alpha + beta , alpha - beta being acute angles prove that tan 2 alpha = (63)/(16).

If alpha, beta are acute angles and cos 2 alpha=(3 cos 2 beta-1)/(3-cos 2 beta) then

If cos alpha =(3)/(5) and cos beta =(5)/(13) and alpha, beta are acute angles, then prove that (a) sin ^(2)((alpha-beta)/(2))=(1)/(65) and (b) cos ^(2)((alpha+beta)/(2))=(16)/(65)

If alpha+beta = 90^@ , prove that sec^2 alpha+sec^2 beta = sec^2 alpha sec^2 beta .