Question

Tan(a+b)=√5,tan(a-b)=1/√3 find angle a nd b

Answer 1

Step-by-step explanation:

$\tan(30) = \frac{1}{ \sqrt{3} } \\ \tan(a - b) = \frac{1}{ \sqrt{3} } \\ \tan(30) = \tan(a - b) \\ a - b = 30 ........1 \\ \tan(45) = 1 \\multiply \: by \: 5 \: on \: both \: sides \\ \tan(45 \times 5) = 1 \times 5 \\ tan(225) = 5 \\ take \: square \: roots \: on \: both \: sides \\ \tan(15) = \sqrt{5} \\ \tan(a + b) = \sqrt{5} \\ \tan(15) = \tan(a + b) \\ a + b = 15 .........2$

We find the two simultaneous equations

Let's solve this

$let \: add \: equation \: 1 \: and \: \: 2 \\ a + b = 15 \\ + \\ a - b = 30 \\ 2a = 45 \\ a = \frac{45}{2} \\ a = 22.5$

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