If `sintheta-costheta=1/2andsin^3theta-cos^3theta=p/q,` where p and q are natural numbers with `HCF=1,`find the value of `((p+q))/3`

if sin theta+cos theta=p and sin^(3)theta+cos^(3)theta=q, then p(p^(2)-3)

If sintheta+costheta=pandsectheta+cosectheta=q , then q(p^(2)-1)=?

Consider alpha, beta ,gamma are the roots of x^(3)-x^(2)-3x+4=0 such that tan^(-1)alpha+tan^(-1)beta+tan^(-1)gamma=theta . If the positive value of tan (theta) is p/q, where p and q are natural numbers, then find the value of (p + q) .

Consider alpha, beta ,gamma are the roots of x^(3)-x^(2)-3x+4=0 such that tan^(-1)alpha+tan^(-1)beta+tan^(-1)gamma=theta . If the positive value of tan (theta) is p/q, where p and q are natural numbers, then find the value of (p + q) .

If sin theta + cos theta = and sin^(3) theta + cos^(3)theta = q, then p(p^(2) - 3) =

If sintheta+costheta=p and sectheta+costheta=q , then prove that q(p^(2)-1)=2p

If sin theta+cos theta=p and sec theta+cos ec theta=q find q(p^(2)-1)=

If sintheta +costheta =p and sectheta+cosectheta=q , show that q(p^2 -1)=2p .

If sintheta+costheta=pandsectheta+"cosec"theta=q then prove that q(p^(2)-1)=2p .

If sintheta+costheta=pandsectheta+"cosec"theta=q then prove that q(p^(2)-1)=2p .