If `alpha in Q_4` and `sin(alpha/2)+cos(alpha/2)=-1/2` then `sin 2alpha=`

If alpha in Q_(4) and (sin alpha)/(2)+(cos alpha)/(2)=-(1)/(2) then sin2 alpha=

If alpha in Q_(4) and "sin" (alpha)/(2) + "cos" (alpha)/(2) = (-1)/(2) "then sin 2" alpha =

If sin alpha/2 + cos alpha/2=1.4 , then: sin alpha cos alpha =

I : If (cos alpha )/(a)=(sin alpha )/(b) then a cos 2 alpha + b cos 2 alpha =a II : If (sin alpha )/(a) =(cos alpha )/(b) then a sin 2 alpha + b cos 2 alpha = a

sin alpha+sin2 alpha+sin4 alpha+sin5 alpha=4cos((alpha)/(2))cos(3(alpha)/(2))sin3 alpha

sin alpha+sin2 alpha+sin4 alpha+sin5 alpha=4cos((alpha)/(2))cos(3(alpha)/(2))sin3 alpha

If a cos^(3)alpha+3a cos alpha sin^(2)alpha=m and a sin^(2)alpha+3a cos^(2)alpha sin alpha=n then (m+n)^((2)/(3))+(m-n)^((2)/(3))=

( cos 2 alpha)/( cos^(4) alpha - sin^(4) alpha ) -(cos^(4) alpha + sin^(4) alpha )/(2-sin^(2) 2alpha ) =

Prove that, (cos alpha + sin alpha)/(cos alpha -sin alpha)-(cos alpha - sin alpha)/(cos alpha + sin alpha) = 2 tan 2 alpha