The value of sin theta + cos theta will be gr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $f(	heta) = \sin 	heta + \cos 	heta$.To find the maximum value,we can rewrite the expression as $f(	heta) = \sqrt{2} \left( \frac{1}{\sqrt

Vedclass · Accepted Answer

$	heta = 45^\circ$

Vedclass · Answer

(B) Let $f(	heta) = \sin 	heta + \cos 	heta$.To find the maximum value,we can rewrite the expression as $f(	heta) = \sqrt{2} \left( \frac{1}{\sqrt{2}} \sin 	heta + \frac{1}{\sqrt{2}} \cos 	heta ight)$.Using the identity $\sin(A+B) = \sin A \cos B + \cos A \sin B$,we get $f(	heta) = \sqrt{2} \sin(	heta + 45^\circ)$.The maximum value of the sine function is $1$,which occurs when the angle is $90^\circ$.Therefore,$\sin(	heta + 45^\circ) = 1$ implies $	heta + 45^\circ = 90^\circ$.Solving for $	heta$,we get $	heta = 90^\circ - 45^\circ = 45^\circ$.

The value of $\sin \theta + \cos \theta$ will be greatest when

Similar Questions

If $\sin \alpha = -\frac{3}{5},$ where $\pi < \alpha < \frac{3\pi}{2},$ then $\cos \frac{\alpha}{2} = $

If $\tan \alpha = n \tan \beta$ and $\sin \alpha = m \sin \beta,$ then $\frac{m^{2}-1}{n^{2}-1} =$

In a triangle,if $\tan A + \tan B + \tan C = 6$ and $\tan A \tan B = 2$,then the values of $\tan A, \tan B,$ and $\tan C$ are:

Which of the following number$(s)$ is/are rational?

$\cos 1^\circ + \cos 2^\circ + \cos 3^\circ + \dots + \cos 180^\circ = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module