ત્રિકોણમિતિય વિધયો — ગણિત ધોરણ 11 સાયન્સ — Question

$\therefore \sin^3\theta+\cos^3\theta+\sin\theta\cos\theta-1=0$

$\therefore (\sin\theta+\cos\theta)(\sin^2\theta-\sin\theta\cos\theta+\cos^2\theta)-(1-\sin\theta\cos\theta)=0$

$\therefore (\sin\theta+\cos\theta)(1-\sin\theta\cos\theta)-(1-\sin\theta\cos\theta)=0$

$\therefore(1-\sin\theta\cos\theta)(\sin\theta+\cos\theta-1)=0$

અહી $1-\sin\theta\cos\theta=0$

$\therefore \sin\theta\cos\theta=1$

$\therefore 2\sin\theta\cos\theta=2$

$\therefore \sin2\theta=2$ જે શક્ય નથી

હવે, $\therefore \sin\theta+cos \theta -1 =0$

$\therefore \sin\theta+\cos\theta=1$

$\therefore \frac{1}{\sqrt{2}}\sin\theta+\frac{1}{\sqrt{2}}\cos\theta=\frac{1}{\sqrt{2}}$

$\therefore \cos\left(\theta-\frac{\pi}{4}\right)=\frac{1}{\sqrt{2}}$

$\theta-\frac{\pi}{4}=2\pi n \pm\frac{\pi}{4},n\in Z$

$\theta=2n\pi,n\in Z$ અથવા $\theta=2n\pi+\frac{\pi}{2},n\in Z$