Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
Given equation is
[tex]2\sin ^2(x)=1-\cos (x)[/tex][tex]\text{ Use }\sin ^2(x)=1-\cos ^2(x).[/tex][tex]2(1-\cos ^2(x))=1-\cos (x)[/tex][tex]2(1^2-\cos ^2(x))=1-\cos (x)[/tex][tex]\text{ Use }1^2-\cos ^2(x)=(1-\cos (x))(1+\cos (x)).[/tex][tex]2(1-\cos (x))(1+\cos (x))=1-\cos (x)[/tex]Cancel out the common term on both sides, we get
[tex]2(1+\cos (x))=1[/tex]Dividing both sides by 2, we get
[tex]1+\cos (x)=\frac{1}{2}[/tex]Subtracting 1 from both sides, we get
[tex]1+\cos (x)-1=\frac{1}{2}-1[/tex][tex]\cos (x)=-\frac{1}{2}[/tex][tex]\text{Use }\cos (\frac{2\pi}{3})=-\frac{1}{2}\text{.}[/tex][tex]\cos (x)=\cos (\frac{2\pi}{3})[/tex][tex]x=\frac{2\pi}{3}[/tex]Hence the exact value of x is
[tex]x=\frac{2\pi}{3}[/tex]The exact values of all angles in the interval [0, pi] that satisfy the given equation is 2pi/3.
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
