proving trig identities
- Thread starter amina786
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Trig Identities
Rule #1 - Do SOMETHING. Don't just stare at it an wonder.
Rule #2 - When in doubt, change everything to sine and cosine.
Rule #3 - If it seems like you are getting nowhere, don't be afraid to back up and pick a new direction.
Rule #1 - Do SOMETHING. Don't just stare at it an wonder.
Rule #2 - When in doubt, change everything to sine and cosine.
Rule #3 - If it seems like you are getting nowhere, don't be afraid to back up and pick a new direction.
mmm4444bot
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I experimented with various identities for about 20 minutes before I found a proof. Like tkhunny says, we need to try stuff first; then we eventually recognize a way second.
I'll show you some of my reasoning.
To start, I factored out -cot(3x) from the last two terms because I thought it would be easier to initially work with the other factors.
cot(x) cot(2x) - cot(3x) [cot(2x) + cot(x)]
Now, you know that the expression in blue is the same as cos(2x)/sin(2x) + cos(x)/sin(x), yes? I combined this into a single ratio.
Also, cot(3x) = cos(3x)/sin(3x), which can be written as cos(x + 2x)/sin(x + 2x).
I used the sum and difference identities to expand both the numerator and denominator of the ratio in red.
When I multiplied the result by the single ratio that I got above, there was a nice cancellation.
At this point, I had the following.
cot(x) cot(2x) + 1 - [cos(x) cos(2x)]/[sin(x) sin(2x)]
This last result is clearly 1.
If you need more help, please show what you've done so far.
I'll show you some of my reasoning.
To start, I factored out -cot(3x) from the last two terms because I thought it would be easier to initially work with the other factors.
cot(x) cot(2x) - cot(3x) [cot(2x) + cot(x)]
Now, you know that the expression in blue is the same as cos(2x)/sin(2x) + cos(x)/sin(x), yes? I combined this into a single ratio.
Also, cot(3x) = cos(3x)/sin(3x), which can be written as cos(x + 2x)/sin(x + 2x).
I used the sum and difference identities to expand both the numerator and denominator of the ratio in red.
When I multiplied the result by the single ratio that I got above, there was a nice cancellation.
At this point, I had the following.
cot(x) cot(2x) + 1 - [cos(x) cos(2x)]/[sin(x) sin(2x)]
This last result is clearly 1.
If you need more help, please show what you've done so far.