Question

The value of sin $\theta cos\theta$ has maximum value when $\theta$ is

• A. ${30}^0$
• B. ${45}^0$
• C. ${60}^0$
• D. ${90}^0$

Answer 1

Answer: (B)

${45}^0$

$Valuesofsin\theta .cos\theta when\theta =0^{\circ }\to 0\times 1=0\theta ={30}^{\circ }\to \frac{1}{2}\times \frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{4}=0.433\theta ={45}^{\circ }\to \frac{1}{\sqrt{2}}\times \frac{1}{\sqrt{2}}=0.5\theta =60^{\circ }\to \frac{\sqrt{3}}{2}\times \frac{1}{2}=0.433\theta =90^{\circ }\to 1\times 0=0\therefore Valueofsin\theta .cos\theta ismaximumat\theta ={45}^{\circ }$