Question

find trigonometry equation

Answer 1

$2 \ cos^{2} x = 3\sin(x) \\ 2(1 - \ { \sin(x) }^{2} ) \\ 2 - 2 { \sin(x) }^{2}$

Answer 2

Answer:

θ = ( 4 n + 1 ) π / 2  where  n ∈  I

Step-by-step explanation:

2 cos² θ = 3 sin θ

we know  cos² θ = 1 - sin² θ

2 (  1 - sin² θ )  = 3 sin θ

2 - 2 sin² θ = 3 sin θ

2 sin² θ + 3 sin θ - 2 = 0

2 sin² θ + 4 sin θ - sin θ - 2 = 0

2 sin θ ( sin θ + 2 ) - ( sin θ + 2 ) = 0

( sin θ + 2 ) ( sin θ - 1 ) = 0

sin θ + 2 = 0  [ This case is not possible ]

Because we know range of sin is -1 to + 1 .

So , we have one case :

sin θ - 1 = 0

sin θ = 1

General solution for sin θ = 1 ;

θ = ( 4 n + 1 ) π / 2  where  n ∈  I

Hence we get answer.