Factorise: 2sin2x−5sin x+3

To factorize the expression 2sin^2(x) - 5sin(x) + 3, we can look for two numbers that multiply to 6 (2*3) and add up to -5. These two numbers are -2 and -3.

Now, we can rewrite the expression as:

2sin^2(x) - 6sin(x) + sin(x) + 3

Next, we can group the terms:

2sin(x)(sin(x) - 3) + 1(sin(x) - 3)

Now, we can factor out the common factor of (sin(x) - 3):

(sin(x) - 3)(2sin(x) + 1)

Therefore, the factored form of 2sin^2(x) - 5sin(x) + 3 is:

(sin(x) - 3)(2sin(x) + 1)