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.

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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)   (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

which clearly simplifies to or

That is not equivalent to

What you undoubtedly meant to write on the RHS was

That expression can be simplified nicely; but it too is NOT equivalent to .
Answer by solver91311(24713)   (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)   (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 . . .


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