sin^(2)theta+sin^(2)(60+theta)+sin^(2)(60-theta)

Prove that sin^(2)theta+sin^(2)2 theta+sin^(2)3 theta+....+sin^(2)n theta=(n)/(2)-(sin n theta cos(n+1)theta)/(2sin theta)

Let f(theta) = sinthetaxx sin(60^@ + theta) sin(60^@ - theta) , then

If cos theta+cos^(2)theta=1 then sin^(2)theta+2sin^(2)theta+sin^(2)theta=

Prove that sin theta sin(60^(@)-theta) sin(60^(@)+theta)=1/4 sin3theta .

Prove that sin theta sin(60^(@)-theta) sin(60^(@)+theta)=1/4 sin3theta .

Prove that sin theta+sin3 theta+sin5 theta+....+sin(2n-1)theta=(sin^(2)n theta)/(sin theta)

Prove that: |sin theta sin(60-theta)sin(60+theta)|<=(1)/(4) for all values of theta