Show that : `sin^6 alpha+ cos^6 alpha ge 1/4`

Show that : sin^4alpha+cos^4alphage 1/2

Show that cos ^2 alpha + cos^2 (alpha +Beta) - 2 cos alpha cos betacos (alpha+ beta) =sin^2 beta

show that : sin^2 alpha + sin^2(alpha +( 2pi)/n) +sin^2(alpha +( 4pi)/n) + ..... n terms = n/2

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

If sin alpha -cos alpha = m , then the value of sin^6alpha+cos^6alpha in terms of m is

Show that: sin^2 alpha + sin^2 beta + 2sinalpha sinbeta cos(alpha+beta)=sin^2 (alpha+beta)

Which is equivalent to (sin^2 alpha + cos^2 alpha )/(cos alpha ) ?

Prove that (sin alpha cos beta + cos alpha sin beta) ^(2) + (cos alpha coa beta - sin alpha sin beta) ^(2) =1.

Prove that sin ( alpha + 30^(@)) = cos alpha + sin (alpha - 30^(@))

Given that sin ^(2) beta = sin alpha cos alpha, show that cos 2 beta=2 cos ^(2) ((pi)/(4) + alpha )).