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Edexcel C3 June 2011 - Proving trigonometry values

Question 6

In part (a) you are given that 1/sin2x-cos2x/sin2x = tanx

In part (b) (i) you are asked

Show that tan15 = 2 - 3^(1/2)

I know you could use the first bit to do 1/sin30 - cos30/sin30 = 1/(1/2) - (root3)/2/(1/2) = 2 - root3

I didn't really pay attention to the hence or otherwise and I tried solving it using the compound angle formula for tan

tan(45-30) = (tan45-tan30)/(1+tan45tan30) = (1-1/root3)/(1+1/root3)

I am not sure how to progress from here, the fractions on fractions have confused me... Any ideas?
Well, in part "a" you'll have shown that tanx = blah blah blah.
So In part "b" i'd sub x=15 into both sides And arrive at the result.


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jamb97
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Original post by Anon123hahaha
Well, in part "a" you'll have shown that tanx = blah blah blah.
So In part "b" i'd sub x=15 into both sides And arrive at the result.


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Okay I don't know if it was clear or not but this is my question: How do you simplify this to tan15 = 2 - root3?

tan(45-30) = (tan45-tan30)/(1+tan45tan30) = (1-1/root3)/(1+1/root3)
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TLDM
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Original post by jamb97
Okay I don't know if it was clear or not but this is my question: How do you simplify this to tan15 = 2 - root3?

tan(45-30) = (tan45-tan30)/(1+tan45tan30) = (1-1/root3)/(1+1/root3)


First, to get rid of the fractions within fractions, multiply the top and bottom of the fraction by sqrt(3). From there you should be able to rationalise the denominator and that should simplify to 2-sqrt(3).
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jamb97
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Original post by TLDM
First, to get rid of the fractions within fractions, multiply the top and bottom of the fraction by sqrt(3). From there you should be able to rationalise the denominator and that should simplify to 2-sqrt(3).
Ah I forgot about rationalizing surds.. Thank you :smile:

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