Question

find acute angle A such that cos27 +cos33 =✓3cosA​

Answer 1

first take cos(a+4b)=0

cos(a+4b)=cos90

(a+4b)=90

now take sin(a+2b)=√3/2

sin(a+2b)=sin60

(a+2b)=60

now subtract eq1 and eq2

we will get b= 15

putting the value of in eq2

we get a=30

Answer 2

$\displaystyle\sf{Given,$

$\displaystyle\sf{cos\:27+cos\:33=\sqrt3\:cos\:A$

$\displaystyle\sf{We\:know\:that\:,$

$\displaystyle\sf{cos\:27+cos\:33=\sqrt3$

$\implies\displaystyle\sf{\sqrt3=\sqrt3\:cos\:A$

$\implies\displaystyle\sf{cos\:A=\frac{\sqrt3}{\sqrt3}$

$\implies\displaystyle\sf{cos\:A=1$

$\implies\displaystyle\sf{A=cos^{-1}(1)$

$\implies\displaystyle\sf{A=0$

$\boxed{\displaystyle\sf{\therefore The\:acute\:angle\:A=0}}$