ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: belb on January 28, 2016, 04:30:40 pm

Title: PLEASE HELP (trig q)
Post by: belb on January 28, 2016, 04:30:40 pm: Hi I've never posted anything not sure if I've even posted this correctly..

I was just wondering how do you simplify the trig tan function when you already have values.
Basically, i have found
tan(x)=√2/4
tan(y)= 2√5/4
therefore: tan(x+y) = √2/4 + 2√5/4 divided by (1-(√10/8)
but i don't know how to simplify the fraction to equal 2(√2 +√5) divided by 3

IF SOMEONE COULD HELP THANK YOU SO MUCH !!!
Title: Re: PLEASE HELP (trig q)
Post by: donglianchun on January 30, 2016, 11:07:33 pm: $\frac{\frac{sqrt{2}}{4}+\frac{2sqrt{5}}{4}}{1-\frac{\sqrt{10}}{8}}$

Multiply both denominator and numerator by 8,

= $\frac{2\sqrt{2}+4\sqrt{5}}{8-\sqrt{10}}$

= $\frac{(2\sqrt{2}+4\sqrt{5})(8+\sqrt{10})}{(8-\sqrt{10})(8+\sqrt{10})}$

= $\frac{16\sqrt{2}+2\sqrt{20}+32\sqrt{5}+4\sqrt{50}}{8^{2}-(\sqrt{10})^{2}}$

= $\frac{16\sqrt{2}+4\sqrt{5}+32\sqrt{5}+20\sqrt{2}}{54}$

= $\frac{36\sqrt{2}+36\sqrt{5}}{54}$

= $\frac{2(\sqrt{2}+\sqrt{5})}{3}$

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