SOLUTION: Simplify the lefthandside so that LHS=RHS 2/sin(b) = sin(b)/cos(b)-1 + sin(b)/cos(b)+1 This is a trig identity and I have no clue how to reach my goal on the left-hand side.

Algebra ->  Proofs -> SOLUTION: Simplify the lefthandside so that LHS=RHS 2/sin(b) = sin(b)/cos(b)-1 + sin(b)/cos(b)+1 This is a trig identity and I have no clue how to reach my goal on the left-hand side.       Log On


   

Question 1112838: Simplify the lefthandside so that LHS=RHS
2/sin(b) = sin(b)/cos(b)-1 + sin(b)/cos(b)+1
This is a trig identity and I have no clue how to reach my goal on the left-hand side.

Found 3 solutions by greenestamps, solver91311, ikleyn:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


No; it is NOT a trig identity -- so you can't prove it.

The RHS as you show it is
sin%28b%29%2Fcos%28b%29-1+%2B+sin%28b%29%2Fcos%28b%29%2B1
which clearly simplifies to 2%2A%28sin%28b%29%2Fcos%28b%29%29 or 2tan%28b%29

That is not equivalent to 2%2Fsin%28b%29

What you undoubtedly meant to write on the RHS was
sin%28b%29%2F%28cos%28b%29-1%29+%2B+sin%28b%29%2F%28cos%28b%29%2B1%29
That expression can be simplified nicely; but it too is NOT equivalent to 2%2Fsin%28b%29.

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


I have to assume that you meant:



because resolving the ambiguities any other way doesn't make any sense. The problem is that the above equation, while it may have a non-null solution set, is not, under any possible definition of the word, an "identity". An identity is a statement that is true for all possible values of the variable.

As a counter-example to your assertion that this is an identity let . Then:



Since and the statement becomes



Which is to say:



Buzz! Sorry, wrong answer. Thank you for playing.

You also have a big problem if or , since either one of those values gives you a zero denominator in the RHS.

So either you wrote the problem incorrectly or your instructor is giving you a trick question. However, no one should have ever referred to what you wrote as an "identity".

John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
Hello, John


when you start your posts with the line

font face="Times New Roman" size="+2"


can you PLEASE then "neutralize" this statement at the end of your post;


otherwise the action of this operator spreads to the next post (to the other posts).


Thank you . . .