`sin alpha=(1)/(2)sqrt(a)sin^(alpha)alpha-4sin^(3)alpha`

sin alpha-cos alpha=(1)/(3) then sin^(4)alpha-cos^(4)alpha=

If A=[cos alpha+sin alpha sqrt(2)sin alpha-sqrt(2)sin alpha cos alpha-sin alpha], prove that =[cos n alpha+sin n alpha sqrt(2)sin n alpha-sqrt(2)sin n alpha cos n alpha-sin n alpha] for all n in N.

If a is any real number then :(sin^(4)alpha+sin^(2)alpha*cos^(2)alpha+cos^(2)alpha)/(sin^(2)alpha+sin^(2)alpha*cos^(2)alpha+sin^(2)alpha)=

If tan((pi)/(4)+(theta)/(2))=tan^(3)((pi)/(4)+(alpha)/(2)) then sin(theta)=(sin(alpha)(3+sin^(2)(alpha)))/(1+3sin^(2)(alpha))

prove that 4sin alpha*sin(alpha+(pi)/(3))*sin(alpha+(2 pi)/(3))=sin3 alpha

Show that 4sin alpha*sin(alpha+(pi)/(3))sin(alpha+2(pi)/(3))=sin3 alpha

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

( sin alpha sin 3alpha + sin 3alpha sin 7 alpha + sin 5 alpha sin 15 alpha )/( sin alpha cos 3 alpha + sin 3alpha cos 7 alpha + sin 5 alpha cos 15 alpha ) =

(sin alpha*sin3 alpha+sin3 alpha*sin7 alpha+sin5 alpha*sin15 alpha)/(sin alpha*cos3 alpha+sin3 alpha cos7 alpha+sin5 alpha*cos15 alpha)=