Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Get detailed and precise answers to your questions from a dedicated community of experts on our Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Proved that the cofunction identity sec([tex]\frac{\pi }{2}[/tex]) - u = csc(u)
We have to prove that the cofunction identity using the addition and subtraction formulas.
sec([tex]\frac{\pi }{2}[/tex]) - u = csc(u)
We can prove this by using the identities given below:
[tex]sec(u)=\frac{1}{cos(u)}[/tex]
[tex]\frac{1}{sin(u)} =csc(u)[/tex]
cos(a-b) = cos a cos b + sin a sin b
Now the explanation,
[tex]sec(\frac{\pi }{2} -u) = csc(u)[/tex]
By using trignometric identities,
[tex]cos(u)=\frac{1}{sec(u)}[/tex] ∴[tex]sec(u)=\frac{1}{cos(u)}[/tex]
So,
[tex]\frac{1}{cos(\frac{\pi }{2}-u) } =csc(u)[/tex]
By substituting the given identities we get,
[tex]\frac{1}{cos(\frac{\pi }{2})cos(u)+sin(\frac{\pi }{2} )sin(u) }[/tex]
= [tex]\frac{1}{0.cos(u)+(1).sin(u)}[/tex]
=[tex]\frac{1}{sin(u)}[/tex]
= csc(u)
csc(u) = csc(u)
Here we proved that the cofunction identity sec([tex]\frac{\pi }{2}[/tex]-u) = csc(u)
Learn more about the cofunction identity here: https://brainly.com/question/17206079
#SPJ4
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.