trigonometry
posted by ajit yadav on .
find acute angle A and B satisfying secAcotBsecA2cotB+2=0

secAcotBsecA2cotB+2=0
(1/cosA)(cosB/sinB)  (1/cosA) 2(cosB/sinB) = 2
multiply each term by sinBcosA
cosB  sinB  2cosBcosA = 2cosAsinB
cosB  sinB  2cosBcosA + 2cosAsinB = 0
(cosB  sinB)  2cosA(cosB  sinB) = 0
(cosB  sinB)(1  2cosA) = 0
cosB = sinB OR 1  2cosA = 0
if cosB = sinB
sinB/cosB = 1
tanB = 1
B = 45° or π/4
if 12cosA = 0
cosA = 1/2
A = 60° or π/3
so A=60° , B= 45°
A=π/3 , B=π/4