Question

For an acute angle $\alpha ,(sin\alpha +\cos \alpha )$ takes the greatest value when the value of $\alpha$ is equal to

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

Answer 1

The correct option is B ${45}^{\circ }$

Let

$y=\sin \alpha +\cos \alpha$

$\frac{dy}{d\alpha }=\cos \alpha -\sin \alpha$

Put $\frac{dy}{d\alpha }=0$ for greatest value

$\cos \alpha -\sin \alpha =0$

$\cos \alpha =\sin \alpha$

$\tan \alpha =1$

$\tan \alpha =\tan \frac{\pi }{4}$

$\alpha =\frac{\pi }{4}={45}^0$

Hence, this is the answer