If `0ltalphaltpi/2` and `sinalpha+cosalpha+tanalpha+cotalpha+secalpha+cosecalpha="7,` then prove that `sin2alpha` is a root of the equation `x^2-44x-36=0.`

If 0 lt alpha lt pi/2 then show that tanalpha+cotalphagtsinalpha+cosalpha

If 0ltalphaltpi/2, show that alpha-alpha^3/3ltsinalpha

If 0ltalphaltpi/2, show that alpha- alpha^3/3ltsinalpha

If p sin^(3)alpha+qcos^(3)alpha=sinalphacosalpha and p sinalpha - q cos alpha=0, then prove that : p^(2)+q^(2)=1

If alpha and beta are the roots of x^(2)+ax+b=0 , then prove that (alpha)/(beta) is a root of the equation bx^(2)+(2b-a^(2))x+b=0

Let alpha, and beta are the roots of the equation x^(2)+x +1 =0 then

Prove that (sinalpha)/(1+cosalpha)+(1+cosalpha)/(sin alpha)=2"cosec "alpha .

If 0ltalphalt pi/4 equation (x-sinalpha)(x-cosalpha)-2=0 has (A) both roots in (sinalpha, cosalpha) (B) both roots in (cosalpha, sinalpha) (C) one root in (-oo, cosalpha) and other in (sinalpha, oo) (D) one root in (-oo,sinalpha) and other in (cosalpha, oo)

If 5tanalpha=4 , show that (5sinalpha-3cosalpha)/(5sinalpha+2cosalpha)=1/6

If (2sinalpha)/(1+cosalpha +sinalpha)=y , then prove that (1-cosalpha+sinalpha )/(1+sinalpha) is also equal to y.