Question

Find the largest value of a cos theta+ b sin (theta+alpha)​

Answer 1

Finding the largest value:

Step-by-step explanation:

$\ Given \ value: \\\\\ a \cos \theta + b \sin (\theta +\alpha) \\\\\ formula:\\\\\sin (\theta +\alpha) = (\sin \theta \cos \alpha +\cos \theta \sin\alpha) \\\\\ Solution:\\\\\ a \cos \theta + b \sin (\theta +\alpha) \\\\\rightarrow \ a \cos \theta + b (\sin \theta \cos \alpha +\cos \theta \sin\alpha) \\\\\rightarrow \ a \cos \theta + b \sin \theta \cos \alpha +b\cos \theta \sin\alpha \\\\\rightarrow (a+b\sin\alpha)\cos \theta + b \cos \alpha\sin \theta$

The largest value is $= \sqrt{(a+b\sin\alpha)^2+(b \cos \alpha)^2}$

$\rightarrow \sqrt{(a^2+b^2\sin^2\alpha+2ab\sin\alpha+b^2 \cos^2 \alpha)} \\\\\rightarrow \sqrt{(a^2+b^2\sin^2\alpha+b^2 \cos^2 \alpha+2ab\sin\alpha)} \\\\\rightarrow \sqrt{(a^2+b^2(\sin^2\alpha+\cos^2 \alpha)+2ab\sin\alpha)} \\\\\rightarrow \sqrt{(a^2+b^2(1)+2ab\sin\alpha)} \\\\\rightarrow \sqrt{(a^2+b^2+2ab\sin\alpha)}$

Learn more:

• Finding the largest value: https://brainly.in/question/5946777