Question

Let S be the sum of all the possible values of sin x that satisfy the following equation:
5-2cos^2(x)-7sin(x) = 0

S can be written as a/b, where a and b are coprime positive integers. What is the value of a + b?

Answer 1

2cos^2(x)=2-2sin^2(x)
substituting,
5-2+2sin^2(x)-7sin(x) = 0
it comes as
2p^2-7p+2=0 where p=sinx
solving
p=13/4,1/4
as sin(x)<=1
so sin(x)=1/4
a=1
b=4
a+b=5

Answer 2

Eh? Starting at

2p^2 - 7p + <b>3</b> = 0
(2p-1)(p-3) = 0
p = 1/2 or 3
but sinx cannot be 3, so
sinx = 1/2 is the only solution

a+b = 1+2 = 3