(sin alpha*sin3 alpha+sin3 alpha*sin7a+sin5 alpha*sin15 alpha)/(sin alpha*cos3 alpha+sin3 alpha cos7 alpha+sin5 alpha*cos15 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)=

( 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 ) =

Prove the following identities: (sin alpha sin 11 alpha + sin 3 alpha sin 7 alpha)/(sin alpha cos 11 alpha + sin 3 alpha cos 7 alpha)= tan 8 alpha

(sqrt2 - sin alpha - cos alpha )/( sin alpha - cos alpha)=

(sqrt2 - sin alpha - cos alpha )/( sin alpha - cos alpha)=

prove that (sin alpha+sin3 alpha+sin5 alpha)/(cos alpha+cos3 alpha+cos5 alpha)=tan3 alpha

tan theta = (sin alpha-cos alpha) / (sin alpha + cos alpha)

((cos alpha-cos3 alpha)(sin8 alpha+sin2 alpha))/((sin5 alpha-sin alpha)(cos4 alpha-cos6 alpha))=

( sin 8 alpha * cos alpha - sin 6 alpha * cos 3 alpha )/(cos 2 alpha cos alpha - sin 3 alpha * sin 4alpha ) =

IF tan alpha = ( sin alpha - cos alpha )/( sin alpha + cos alpha) , then sin alpha + cos alpha is