Question

If $sin\theta ,cos\theta$ are the roots of the equation $2x^2-2\sqrt{2}x+1=0$, then $\theta$ is equal to

• A. ${15}^o$
• B. ${30}^o$
• C. ${45}^o$
• D. ${60}^o$

Answer 1

Answer: (C)

${45}^o$

$2x^2-2\sqrt{2}x+1=0$

Given $sin\theta ,cos\theta$ are the roots,

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

and $sin\theta .cos\theta =\frac{1}{2}\Rightarrow sin2\theta =1$

$sin2\theta =sin{90}^{\circ }\Rightarrow 2\theta ={90}^{\circ }$

Hence solution is, $\theta ={45}^{\circ }$