# Thread: trigo>find angle

1. ## trigo>find angle

cos(A-30*)=3cos(A+30*)

how to do???i stuck at beginning.

THX FOR WHO HELP~

2. Originally Posted by sanikui
cos(A-30*)=3cos(A+30*)

how to do???i stuck at beginning.

THX FOR WHO HELP~
Do you know these formulae:

$\displaystyle cos (A + B)= cosA cosB - sinA sinB$

$\displaystyle cos (A - B) = cosA cosB + sinA sinB$

Now apply these formulae and see here,

cos (A - 30) = 3 cos (A + 30)

$\displaystyle \Rightarrow cosA cos30 + sinA sin30 = 3(cosA cos30 - sinA sin30)$

$\displaystyle \Rightarrow cosA cos30 + sinA sin30 - 3cosA cos30 - 3sinA sin30 = 0$

$\displaystyle \Rightarrow -2cosA cos30 + 4sinA sin30 = 0$

$\displaystyle \Rightarrow -2cosA \left(\frac{\sqrt{3}}{2}\right) + 4sinA \left(\frac{1}{2}\right) = 0$

$\displaystyle \Rightarrow -\sqrt{3} \;cosA + 2sinA = 0$

$\displaystyle \Rightarrow 2sinA = \sqrt{3} \;cosA$

$\displaystyle \Rightarrow \frac {sinA}{cosA} = \frac{\sqrt{3}}{2}$

$\displaystyle \Rightarrow tanA = \frac{\sqrt{3}}{2}$

$\displaystyle \Rightarrow tanA = 0.866$

$\displaystyle A = 41\;\;degrees$

3. Originally Posted by Shyam
Do you know these formulae:

$\displaystyle cos (A + B)= cosA cosB - sinA sinB$

$\displaystyle cos (A - B) = cosA cosB + sinA sinB$

Now apply these formulae and see here,

cos (A - 30) = 3 cos (A + 30)

$\displaystyle \Rightarrow cosA cos30 + sinA sin30 = 3(cosA cos30 - sinA sin30)$

$\displaystyle \Rightarrow cosA cos30 + sinA sin30 - 3cosA cos30 - 3sinA sin30 = 0$

$\displaystyle \Rightarrow -2cosA cos30 + 4sinA sin30 = 0$

$\displaystyle \Rightarrow -2cosA \left(\frac{\sqrt{3}}{2}\right) + 4sinA \left(\frac{1}{2}\right) = 0$

$\displaystyle \Rightarrow -\sqrt{3} \;cosA + 2sinA = 0$

$\displaystyle \Rightarrow 2sinA = \sqrt{3} \;cosA$

$\displaystyle \Rightarrow \frac {sinA}{cosA} = \frac{\sqrt{3}}{2}$

$\displaystyle \Rightarrow tanA = \frac{\sqrt{3}}{2}$

$\displaystyle \Rightarrow tanA = 0.866$

$\displaystyle A = 41\;\;degrees$
Yes, the answer is right. But the answer got 2 angles. Becouse tangent positive in 1st and 3rd quadrant.
A=41* and 221*
thx thx V^^