SOLUTION: for sinA +cosAcotA=cscA a.Show that the equation is true whenA=30 degrees. use exact values b.prove the equation algebraically c.state any restrictions to the equation

Algebra ->  Trigonometry-basics -> SOLUTION: for sinA +cosAcotA=cscA a.Show that the equation is true whenA=30 degrees. use exact values b.prove the equation algebraically c.state any restrictions to the equation      Log On


   

Question 30138: for sinA +cosAcotA=cscA
a.Show that the equation is true whenA=30 degrees. use exact values
b.prove the equation algebraically
c.state any restrictions to the equation
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
For part a; to do this first switch your calculator into radians mode and then calculate:
sin(30)+cos(30)(cos[30]/sin[30])=1/sin(30)
-0.988+(0.154)(-0.156)=1.01
1.01=1.01

For part b put the equation into simplier steps:
SinA%2BCosA%28CosA%2FSinA%29=1%2FSinA --> deal with the left side:
SinA%2B%28Cos%5E2%28A%29%29%2FSinA
Multiply the SinA by SinA to get a common denomenator:
%28Sin%5E2%28A%29%2Bcos%5E2%28A%29%29%2FSinA
Use Pathagorean identity:
1%2FSinA
L.S. = R.S and Hence, proven:
Paul.