A community for students.
Here's the question you clicked on:
 0 viewing
AaronAndyson
 one year ago
Prove that secA(1sinA)(secA+tanA)=1?
AaronAndyson
 one year ago
Prove that secA(1sinA)(secA+tanA)=1?

This Question is Closed

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0here we have to use these identities: \[\Large \sec A = \frac{1}{{\cos A}},\quad \tan A = \frac{{\sin A}}{{\cos A}}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0hint: we can write this step: \[\Large \begin{gathered} \sec A\left( {1  \sin A} \right)\left( {\sec A + \tan A} \right) = \hfill \\ \hfill \\ = \frac{1}{{\cos A}}\left( {1  \sin A} \right)\left( {\frac{1}{{\cos A}} + \frac{{\sin A}}{{\cos A}}} \right) = ...? \hfill \\ \end{gathered} \] please, simplify

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0I have replaced secA wit 1/cosA and tanA with (sinA)/(cosA)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0hint: \[\Large \begin{gathered} \sec A\left( {1  \sin A} \right)\left( {\sec A + \tan A} \right) = \hfill \\ \hfill \\ = \frac{1}{{\cos A}}\left( {1  \sin A} \right)\left( {\frac{1}{{\cos A}} + \frac{{\sin A}}{{\cos A}}} \right) = \hfill \\ \hfill \\ = \frac{{1  \sin A}}{{\cos A}} \cdot \frac{{1 + \sin A}}{{\cos A}} = ...? \hfill \\ \end{gathered} \] now it is easy to write the next step

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0you have to multiply those two fractions

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.0hint: \[\large \begin{gathered} \sec A\left( {1  \sin A} \right)\left( {\sec A + \tan A} \right) = \hfill \\ \hfill \\ = \frac{1}{{\cos A}}\left( {1  \sin A} \right)\left( {\frac{1}{{\cos A}} + \frac{{\sin A}}{{\cos A}}} \right) = \hfill \\ \hfill \\ = \frac{{1  \sin A}}{{\cos A}} \cdot \frac{{1 + \sin A}}{{\cos A}} = \hfill \\ \hfill \\ = \frac{{\left( {1  \sin A} \right)\left( {1 + \sin A} \right)}}{{{{\left( {\cos A} \right)}^2}}} = ...? \hfill \\ \end{gathered} \]

AaronAndyson
 one year ago
Best ResponseYou've already chosen the best response.01sin^2/cos^2 is 1

AaronAndyson
 one year ago
Best ResponseYou've already chosen the best response.0thanks help me more?
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.