If sin q and cos q are the roots of the equation ax2 +bx + c = 0, then

Since sin q and cos q are the roots of the equation  ax2 +bx + c = 0∴ sin⁡θ+cos⁡θ=−baandsin⁡θcos⁡θ=caNow (sin⁡θ+cos⁡θ)2=1+2sin⁡θcos⁡θ∴b2a2=1+2ca=a+2ca∴ b2=a(a+2c)=a2+2ac⇒b2+c2=a2+2ac+c2=(a+c)2⇒(a+c)2=b2+c2