SOLUTION: If tan theata =1 then find sin theata Ścos theata

Algebra ->  Trigonometry-basics -> SOLUTION: If tan theata =1 then find sin theata Ścos theata      Log On


   

Question 937801: If tan theata =1 then find sin theata Ścos theata
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
For any angle theta ,
%28sin%28theta%29%29%5E2%2B%28cos%28theta%29%29%5E2=1 .
Also, for any angle theta with cos%28theta%29%3C%3E0 ,
tan%28theta%29 exists, and
tan%28theta%29=sin%28theta%29%2Fcos%28theta%29

In this case,
tan%28theta%29=sin%28theta%29%2Fcos%28theta%29=1--->sin%28theta%29=cos%28theta%29 .
Then,
---> 2%28sin%28theta%29%29%5E2=2%28cos%28theta%29%29%5E2=1 ---> %28sin%28theta%29%29%5E2=%28cos%28theta%29%29%5E2=1%2F2 ---> sin%28theta%29=cos%28theta%29=sqrt%281%2F2%29=sqrt%282%29%2F2 .
So,
sin%28theta%29%2Acos%28theta%29=sqrt%281%2F2%29%2Asqrt%281%2F2%29=highlight%281%2F2%29