Westonci.ca is the best place to get answers to your questions, provided by a community of experienced and knowledgeable experts. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Answer:
tan²Θ
Step-by-step explanation:
simplify the expression using the identities
secΘ = [tex]\frac{1}{cos0}[/tex]
tan²Θ = sec²Θ - 1
then
[tex]\frac{cos0-cos^30}{cos^30}[/tex] ( divide each term on the numerator by cos³Θ
= [tex]\frac{cos0}{cos^30}[/tex] - [tex]\frac{cos^30}{cos^30}[/tex]
= [tex]\frac{1}{cos^20}[/tex] - 1
= sec²Θ - 1
= tan²Θ
Answer:
[tex]\tan^2(\theta)[/tex]
Step-by-step explanation:
Assuming this is
[tex]\dfrac{\cos(\theta)-cos^3(\theta)}{cos^3(\theta)}[/tex]
Trig identities used:
[tex]\sin^2(\theta)+\cos^2(\theta)=1 \implies 1-\cos^2(\theta)=\sin^2(\theta)[/tex]
[tex]\dfrac{\cos(\theta)-cos^3(\theta)}{cos^3(\theta)}[/tex]
[tex]=\dfrac{\cos(\theta)(1-cos^2(\theta))}{cos^3(\theta)}[/tex]
[tex]=\dfrac{1-cos^2(\theta)}{cos^2(\theta)}[/tex]
[tex]=\dfrac{sin^2(\theta)}{cos^2(\theta)}[/tex]
[tex]=\tan^2(\theta)[/tex]
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.