Question

Solve the equation (2+sin A)/(2-cos A) = 2 where 0 <= A <= 180. Given the answers correct to the near 0.1 if necessary.

Answer 1

lets this way
cross multiply:-

2 + sin A = 4 - 2 cos A
sin A + 2 cos A = 2

Answer 2

its been a long time since I did these
hold on a second while a look it up

Answer 3

OK you need to write this in the form R(sin(A + B) where B is the complementary angle

Answer 4

SInA + 2cosA = RsinAcosB + RsinBcosA

equating coefficients of sinA and cosA

sinA; 1 = RcosB
cosA: 2 = RsinB

Answer 5

so tan B = RsinB / RcosB = 2

making B = 63.43 degrees
and R = square root of the sum of the coefficients of cos A and SinA
= sqrt(1^2+2^2) = sqrt5

Answer 6

so we get
sqrt5(A + 63.43) = 2

Answer 7

from this you can find the value of A

Answer 8

oops sorry that should be
sqrt5 sin( A + 63.43) = 2

Answer 9

lol - I'm looking at the original equation and I see you can get one solution just by inspection.
sin 0 = 0 and cos 0 = 1

so plugging this in
(2 + 0) / (2 - 1) = 2

so A = 0 is one solution

Answer 10

thats the only solution 180 wont fit because cos 180 = -1