Question

For an acute angle $\theta ,\sin \theta +\cos \theta$ takes the greatest value when $\theta$ is

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

Answer 1

Answer: (B)

${45}^0$

Let $f\left(x\right)=\sin \theta +\cos \theta$

$f^{\prime }\left(x\right)=\cos \theta -\sin \theta$

For maximum value of $f\left(x\right)$

$f^{\prime }\left(x\right)=0$

or, $\cos \theta -\sin \theta =0$

or, $\tan \theta =1$

or, $\theta ={45}^{\circ }$

Hence, B is the correct option.